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A lognormal type stochastic volatility model with quadratic driftAug 20 2019This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant ... More

Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option ValuationAug 15 2019Despite being described as a medium of exchange, cryptocurrencies do not have the typical attributes of a medium of exchange. Consequently, cryptocurrencies are more appropriately described as crypto assets. A common investment attribute shared by the ... More

Nonparametric modeling cash flows of insurance companyAug 14 2019The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including policies with deductible) ... More

Dynamic Dependence Modeling in financial time seriesAug 14 2019This paper explores the dependence modeling of financial assets in a dynamic way and its critical role in measuring risk. Two new methods, called Accelerated Moving Window method and Bottom-up method are proposed to detect the change of copula. The performance ... More

Performance of tail hedged portfolio with third moment variation swapAug 14 2019The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap ... More

Computational method for probability distribution on recursive relationships in financial applicationsAug 14 2019In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging error, the Asian ... More

Forecast Encompassing Tests for the Expected ShortfallAug 13 2019In this paper, we introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). Forecasting and forecast evaluation techniques for the ES are rapidly gaining attention through the recently introduced Basel III Accords, which ... More

Latency and Liquidity RiskAug 08 2019Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo ... More

Risk-Control StrategiesAug 06 2019In this paper, we consider the pricing of derivative products that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), Guaranteed investment certificate (GIC), American and Barrier options are ... More

Stochastic ordering of Gini indexes for multivariate elliptical random variablesAug 06 2019In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components ... More

Strategic Payments in Financial NetworksAug 05 2019In their seminal work on systemic risk in financial markets, Eisenberg and Noe proposed and studied a model with $n$ firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent ... More

calculation worst-case Value-at-Risk prediction using empirical data under model uncertaintyAug 02 2019Quantification of risk positions under model uncertainty is of crucial importance from both viewpoints of external regulation and internal management. The concept of model uncertainty, sometimes also referred to as model ambiguity. Although we know the ... More

A full and synthetic model for Asset-Liability Management in life insurance, and analysis of the SCR with the standard formulaAug 02 2019The aim of this paper is to introduce a synthetic ALM model that catches the main specificity of life insurance contracts. First, it keeps track of both market and book values to apply the regulatory profit sharing rule. Second, it introduces a determination ... More

A procedure for loss-optimising default definitions across simulated credit risk scenariosJul 29 2019A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative ... More

Algorithmic market making: the case of equity derivativesJul 29 2019In this article, we tackle the problem of a market maker in charge of a book of equity derivatives on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic ... More

Algorithmic market making: the case of equity derivativesJul 29 2019Jul 30 2019In this article, we tackle the problem of a market maker in charge of a book of equity derivatives on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic ... More

Algorithmic market making: the case of equity derivativesJul 29 2019Aug 06 2019In this article, we tackle the problem of a market maker in charge of a book of equity derivatives on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic ... More

SlideVaR: a risk measure with variable risk attitudesJul 27 2019To find a trade-off between profitability and prudence, financial practitioners need to choose appropriate risk measures. Two key points are: Firstly, investors' risk attitudes under uncertainty conditions should be an important reference for risk measures. ... More

On the Statistical Differences between Binary Forecasts and Real World PayoffsJul 24 2019What do binary (or probabilistic) forecasting abilities have to do with overall performance? We map the difference between (univariate) binary predictions, bets and "beliefs" (expressed as a specific "event" will happen/will not happen) and real-world ... More

Multivariate Modeling of Natural Gas Spot Trading Hubs Incorporating Futures Market Realized VolatilityJul 23 2019Financial markets for Liquified Natural Gas (LNG) are an important and rapidly-growing segment of commodities markets. Like other commodities markets, there is an inherent spatial structure to LNG markets, with different price dynamics for different points ... More

A note on Parisian ruin under a hybrid observation schemeJul 23 2019In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. \cite{binetal2016}. Under this model, the process is observed at Poisson arrival times whenever the business is financially healthy ... More

Poissonian occupation times of spectrally negative Lévy processes with applicationsJul 23 2019In this paper, we introduce the concept of \emph{Poissonian occupation times} below level $0$ of spectrally negative L\'evy processes. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an ... More

A simulation of the insurance industry: The problem of risk model homogeneityJul 12 2019We develop an agent-based simulation of the catastrophe insurance and reinsurance industry and use it to study the problem of risk model homogeneity. The model simulates the balance sheets of insurance firms, who collect premiums from clients in return ... More

Mathematical Analysis of Dynamic Risk Default in MicrofinanceJul 10 2019In this work we will develop a new approach to solve the non repayment problem in microfinance due to the problem of asymmetric information. This approach is based on modeling and simulation of ordinary differential systems where time remains a primordial ... More

Improving Detection of Credit Card Fraudulent Transactions using Generative Adversarial NetworksJul 07 2019In this study, we employ Generative Adversarial Networks as an oversampling method to generate artificial data to assist with the classification of credit card fraudulent transactions. GANs is a generative model based on the idea of game theory, in which ... More

Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin TheoryJul 03 2019We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain ... More

P2P Loan acceptance and default prediction with Artificial IntelligenceJul 03 2019Logistic Regression and Support Vector Machine algorithms, together with Linear and Non-Linear Deep Neural Networks, are applied to lending data in order to replicate lender acceptance of loans and predict the likelihood of default of issued loans. A ... More

Elicitability and Identifiability of Systemic Risk Measures and other Set-Valued FunctionalsJul 02 2019This paper is concerned with a two-fold objective. Firstly, we establish elicitability and identifiability results for systemic risk measures introduced in Feinstein, Rudloff and Weber (2017). Specifying the entire set of capital allocations adequate ... More

Adaptive Pricing in Insurance: Generalized Linear Models and Gaussian Process Regression ApproachesJul 02 2019We study the application of dynamic pricing to insurance. We view this as an online revenue management problem where the insurance company looks to set prices to optimize the long-run revenue from selling a new insurance product. We develop two pricing ... More

Tracking VIX with VIX Futures: Portfolio Construction and PerformanceJun 29 2019We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. ... More

Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading ConstraintsJun 28 2019We develop a dual control method for approximating investment strategies in incomplete environments that emerge from the presence of market frictions. Convex duality enables the approximate technology to generate lower and upper bounds on the optimal ... More

A Triptych Approach for Reverse Stress Testing of Complex PortfoliosJun 26 2019The quest for diversification has led to an increasing number of complex funds with a high number of strategies and non-linear payoffs. The new generation of Alternative Risk Premia (ARP) funds are an example that has been very popular in recent years. ... More

A simple approach to dual representations of systemic risk measuresJun 26 2019We describe a general approach to obtain dual representations for systemic risk measures of the "allocate first, then aggregate"-type, which have recently received significant attention in the literature. Our method is based on the possibility to express ... More

Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected ShortfallJun 24 2019Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty ... More

A Model of the Optimal Selection of Crypto AssetsJun 23 2019We propose a modelling framework for the optimal selection of crypto assets. Crypto assets differ by two essential features: security (technological) and stability (governance). Investors make choices over crypto assets similarly to how they make choices ... More

Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected ShortfallJun 21 2019A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and the latent ... More

When Risks and Uncertainties Collide: Mathematical Finance for Arbitrage Markets in a Quantum Mechanical ViewJun 15 2019Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting ... More

Variants of the Smith-Wilson method with a view towards applicationsJun 14 2019We propose two variants of the Smith-Wilson method for practical application in the insurance industry. Our first variant relaxes the Smith-Wilson energy and can be used to incorporate less reliable market data with a certain weight rather than disregarding ... More

Stochastic PDEs for large portfolios with general mean-reverting volatility processesJun 13 2019In this article we consider a large structural market model of defaultable assets, where the asset value processes are modelled by using stochastic volatility models with default upon hitting a lower boundary. The volatility processes are picked from ... More

Neural Learning of Online Consumer Credit RiskJun 05 2019This paper takes a deep learning approach to understand consumer credit risk when e-commerce platforms issue unsecured credit to finance customers' purchase. The "NeuCredit" model can capture both serial dependences in multi-dimensional time series data ... More

Fair Pricing of Variable Annuities with Guarantees under the Benchmark ApproachJun 04 2019In this paper we consider the pricing of variable annuities (VAs) with guaranteed minimum withdrawal benefits. We consider two pricing approaches, the classical risk-neutral approach and the benchmark approach, and we examine the associated static and ... More

Two Resolutions of the Margin Loan Pricing PuzzleJun 03 2019This paper supplies two possible resolutions of Fortune's (2000) margin-loan pricing puzzle. Fortune (2000) noted that the margin loan interest rates charged by stock brokers are very high in relation to the actual (low) credit risk and the cost of funds. ... More

The Laws of Motion of the Broker Call Rate in the United StatesJun 03 2019In this paper, which is the third installment of the author's trilogy on margin loan pricing, we analyze $1,367$ monthly observations of the U.S. broker call money rate, which is the interest rate at which stock brokers can borrow to fund their margin ... More

Portfolio diversification based on ratios of risk measuresJun 03 2019A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance theory and other known portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality and ultimately ... More

Portfolio diversification based on ratios of risk measuresJun 03 2019Jun 05 2019A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance theory and other known portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality and ultimately ... More

Understanding Distributional Ambiguity via Non-robust Chance ConstraintJun 03 2019The choice of the ambiguity radius is critical when an investor uses the distributionally robust approach to address the issue that the portfolio optimization problem is sensitive to the uncertainties of the asset return distribution. It cannot be set ... More

Optimal Dynamic Strategies on Gaussian ReturnsMay 31 2019Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters ... More

The Network Effect in Credit Concentration RiskMay 31 2019Measurement and management of credit concentration risk is critical for banks and relevant for micro-prudential requirements. While several methods exist for measuring credit concentration risk within institutions, the systemic effect of different institutions' ... More

Cross-sectional Learning of Extremal Dependence among Financial AssetsMay 31 2019We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random ... More

An assets-liabilities dynamical model of banking system and systemic risk governanceMay 29 2019We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the difference between ... More

How big should a Stress Shock be?May 24 2019Stress shocks are often calculated as multiples of the standard deviation of a history set. This paper investigates how many standard deviations are required to guarantee that this shock exceeds any observation within the history set, given the additional ... More

Real-time Prediction of Bitcoin Bubble CrashesMay 23 2019Jun 13 2019In the past decade, Bitcoin as an emerging asset class has gained widespread public attention because of their extraordinary returns in phases of extreme price growth and their unpredictable massive crashes. We apply the log-periodic power law singularity ... More

Real-time Prediction of Bitcoin bubble CrashesMay 23 2019In the past decade, Bitcoin has become an emerging asset class well known to most people because of their extraordinary return potential in phases of extreme price growth and their unpredictable massive crashes. We apply the LPPLS confidence indicator ... More

Variable annuities in a Lévy-based hybrid model with surrender riskMay 23 2019This paper proposes a market consistent valuation framework for variable annuities with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and uses time-inhomogeneous ... More

Testing Sharpe ratio: luck or skill?May 20 2019May 21 2019Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation. However, the elements ... More

Spectral risk measures and uncertaintyMay 19 2019Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we propose a Deviation-based ... More

What is the Minimal Systemic Risk in Financial Exposure Networks?May 15 2019Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis, systemic ... More

Reduced Form Capital OptimizationMay 15 2019We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This reduced form ... More

ERRATUM: Stochastic evolution equations for large portfolios of stochastic volatility modelsMay 10 2019In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then we redevelop ... More

Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolationMay 01 2019We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev method delivers ... More

Avoiding Backtesting Overfitting by Covariance-Penalties: an empirical investigation of the ordinary and total least squares casesMay 01 2019Systematic trading strategies are rule-based procedures which choose portfolios and allocate assets. In order to attain certain desired return profiles, quantitative strategists must determine a large array of trading parameters. Backtesting, the attempt ... More

Risk measures and progressive enlargement of filtration: a BSDE approachApr 30 2019We consider dynamic risk measures induced by Backward Stochastic Differential Equations (BSDE) in enlargement of filtration setting. On a fixed probability space, we are given a standard Brownian motion and a pair of random variables $(\tau, \zeta) \in ... More

Tail models and the statistical limit of accuracy in risk assessmentApr 27 2019In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is unknown, the database ... More

Optimal investment strategy for DC pension plans with stochastic force of mortalityApr 23 2019This paper studies an optimal portfolio problem for a DC pension plan considering both interest rate risk and longevity risk. In the accumulation phase, plan members pay constant contributions continuously into the pension fund. We assume that the evolution ... More

Simulation-based Value-at-Risk for Nonlinear PortfoliosApr 19 2019Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness, however, substantially ... More

The Black-Scholes Equation in Presence of ArbitrageApr 17 2019Jun 26 2019We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional It\^o's process we specify and prove ... More

The Black-Scholes Equation in Presence of ArbitrageApr 17 2019Jun 19 2019We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional It\^o's process we specify and prove ... More

The Black-Scholes Equation in Presence of ArbitrageApr 17 2019We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional It\^o's process we specify and prove ... More

Loss-based risk statistics with set-valued analysisApr 16 2019Since the portfolio has become a hot topic, we wii introduce a special risk statistics from the perspective of loss. This new risk statistic can be uesd for the quantification of portfolio risk. Representation results are provided. Finally, examples are ... More

Loss-based risk statistics with scenario analysisApr 16 2019Since the investors and regulators pay more attention to losses rather than gains, we will study a new class of risk statistics, named loss-based risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension ... More

Cash sub-additive risk statistics with scenario analysisApr 16 2019Since the money is of time value, we will study a new class of risk statistics, named cash sub-additive risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, ... More

Tail probabilities of random linear functions of regularly varying random vectorsApr 15 2019We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random ... More

Deep Generative Models for Reject Inference in Credit ScoringApr 12 2019Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. In this ... More

Optimal excess-of-loss reinsurance for stochastic factor risk modelsApr 10 2019We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed by a marked ... More

A Thermodynamic Picture of Financial Market and Model RiskMar 30 2019By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused by model uncertainty ... More

Portfolio optimization with two coherent risk measuresMar 25 2019Aug 12 2019We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio manager is ... More

Portfolio optimization with two coherent risk measuresMar 25 2019We provide a closed-form analytical solution to a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio ... More

A Machine Learning approach to Risk Minimisation in Electricity Markets with Coregionalized Sparse Gaussian ProcessesMar 22 2019The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key factor explaining ... More

A Machine Learning approach to Risk Minimisation in Electricity Markets with Coregionalized Sparse Gaussian ProcessesMar 22 2019Apr 03 2019The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key factor explaining ... More

Computation of systemic risk measures: a mixed-integer linear programming approachMar 20 2019Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures ... More

Risk and Return models for Equity Markets and Implied Equity Risk PremiumMar 18 2019Equity risk premium is a central component of every risk and return model in finance and a key input to estimate costs of equity and capital in both corporate finance and valuation. An article by Damodaran examines three broad approaches for estimating ... More

Optimal FX Hedge Tenor with Liquidity RiskMar 15 2019We develop an optimal currency hedging strategy for fund managers who own foreign assets to choose the hedge tenors that maximize their FX carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged ... More

Machine Learning Risk ModelsMar 15 2019We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning ... More

Machine Learning Risk ModelsMar 15 2019Apr 09 2019We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning ... More

A lending scheme for a system of interconnected banks with probabilistic constraints of failureMar 14 2019We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of a bank. The solution can be applied to a network of banks providing a general solution when aforementioned probability ... More

Altcoin-Bitcoin ArbitrageMar 13 2019Apr 02 2019We give an algorithm and source code for a cryptoasset statistical arbitrage alpha based on a mean-reversion effect driven by the leading momentum factor in cryptoasset returns discussed in https://ssrn.com/abstract=3245641. Using empirical data, we identify ... More

Altcoin-Bitcoin ArbitrageMar 13 2019We give an algorithm and source code for a cryptoasset statistical arbitrage alpha based on a mean-reversion effect driven by the leading momentum factor in cryptoasset returns discussed in https://ssrn.com/abstract=3245641. Using empirical data, we identify ... More

Nonlinear expectations of random setsMar 12 2019Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions ... More

Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its SourceMar 10 2019Since the introduction of risk-based solvency regulation, pro-cyclicality has been a subject of concerns from all market participants. Here, we lay down a methodology to evaluate the amount of pro-cyclicality in the way financial institutions measure ... More

On occupation times in the red of Lévy risk modelsMar 09 2019Jul 23 2019In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally negative L\'{e}vy ... More

On occupation times in the red of Lévy risk modelsMar 09 2019In this paper, we complement the existing literature on the occupation time in the red (below level $0$) of a spectrally negative L\'evy process, and later extend the analysis to the refracted spectrally negative L\'evy process. For both classes of processes, ... More

Kernel Based Estimation of Spectral Risk MeasuresMar 08 2019Spectral risk measures (SRMs) belongs to the family of coherent risk measures. A natural estimator for the class of spectral risk measures (SRMs) has the form of $L$-statistics. In the literature, various authors have studied and derived the asymptotic ... More

Fair Capital Risk AllocationFeb 26 2019In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular ... More

Statistical arbitrage of coherent risk measuresFeb 26 2019We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability if the market admits statistical arbitrage opportunities which we term $\rho$-arbitrage for a risk measure $\rho$. We show how to determine ... More

Controlling systemic risk - network structures that minimize it and node properties to calculate itFeb 22 2019Evaluation of systemic risk in networks of financial institutions in general requires information of inter-institution financial exposures. In the framework of Debt Rank algorithm, we introduce an approximate method of systemic risk evaluation which requires ... More

Revising SA-CCRFeb 22 2019Apr 08 2019From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market Model

From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market ModelFeb 22 2019SA-CCR has major issues including: lack of self-consistency for linear trades; lack of appropriate risk sensitivity (zero positions can have material add-ons; moneyness is ignored); dependence on economically-equivalent confirmations. We show that SA-CCR ... More

Risk Management with Tail Conditional Certainty EquivalentsFeb 19 2019Certainty Equivalent is a utility-based measure that performs as a measure in which investors are indifferent between this measure and investment that holds some uncertainty. Therefore, it plays an essential role in utility-based decision making. One ... More

Risk Management with Tail Quasi-Linear MeansFeb 19 2019Jul 15 2019We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the Entropic Risk ... More

Risk management with machine-learning-based algorithmsFeb 14 2019We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting strategies ... More