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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
Derivative of a Conic Problem with a Unique SolutionMar 13 2019We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function ... More
The fractional and mixed-fractional CEV modelMar 13 2019The continuous observation of the financial markets has identified some 'stylized facts' which challenge the conventional assumptions, promoting the born of new approaches. On one hand, the long range dependence has been faced replacing the traditional ... More
Optimal Information Acquisition and Consumption Under Habit Formation PreferenceMar 11 2019We consider a model of two-stage optimal decision making involving pure information learning beforehand and dynamic consumption afterwards: in stage-1 from initial time to a chosen stopping time, the individual investor has access to full market information ... More
Affine term structure models : a time-changed approach with perfect fit to market curvesMar 11 2019We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross ... More
Fine Properties of the Optimal Skorokhod Embedding ProblemMar 09 2019We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set $\mathcal{T}(\nu)$ ... More
Asymptotics for volatility derivatives in multi-factor rough volatility modelsMar 07 2019We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical ... More
Strict Local Martingales and the Khasminskii test for ExplosionsMar 06 2019We exhibit sufficient conditions such that components of a multidimensional SDE giving rise to a local martingale $M$ are strict local martingales or martingales. We assume that the equations have diffusion coefficients of the form $\sigma(M_t,v_t),$ ... More
Cover's Rebalancing Option With Discrete Hindsight OptimizationMar 03 2019We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set ... More
Non-Parametric Robust Model Risk Measurement with Path-Dependent Loss FunctionsMar 02 2019Understanding and measuring model risk is important to financial practitioners. However, there lacks a non-parametric approach to model risk quantification in a dynamic setting and with path-dependent losses. We propose a complete theory generalizing ... More
A convex duality approach for pricing contingent claims under partial information and short selling constraintsFeb 27 2019We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our primal problem, ... 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
Multiscale Asymptotic Analysis for Portfolio Optimization under Stochastic EnvironmentFeb 19 2019Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization problem in a Markovian ... More
Elicitability of Range Value at RiskFeb 12 2019The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring functions should be (strictly) consistent for ... More
Implementation of a Port-graph Model for FinanceFeb 06 2019In this paper we examine the process involved in the design and implementation of a port-graph model to be used for the analysis of an agent-based rational negligence model. Rational negligence describes the phenomenon that occurred during the financial ... More
Foundations of a pathwise volatility framework with explicit fast reversion limitsFeb 05 2019Our first main results are the existence and uniqueness of solutions to a `generalised CIR initial-value problem', which originates from the classical Cox-Ingersoll-Ross (CIR) stochastic differential equation after a time-change. These results hold on ... More
Strong convergence rates for Markovian representations of fractional Brownian motionFeb 04 2019Feb 15 2019Fractional Brownian motion can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily ... More
Strong convergence rates for numerical approximations of fractional Brownian motionFeb 04 2019Fractional Brownian motion can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily ... More
Optimal market making under partial information with general intensitiesFeb 04 2019Starting from the Avellaneda--Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time interval, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads ... More
The Applications of Graph Theory to InvestingFeb 02 2019How can graph theory be applied to investing in the stock market? The answer may help investors realize the true risks of their investments, help prevent recessions like that of 2008, and increase financial literacy amongst students. Using several original ... More
Stochastic control in high-dimensional statistical arbitrage under an Ornstein-Uhlenbeck processJan 27 2019The present paper aims to provide the first systematic study of high-dimensional statistical arbitrage using both factor models and tools from stochastic control theory, obtaining closed-form optimal strategies in most cases and extending in multiple ... More
Erratum: Higher Order Elicitability and Osband's PrincipleJan 25 2019This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
Lattice investment projects support process model with corruptionJan 25 2019Lattice investment projects support process model with corruption is formulated and analyzed. The model is based on the Ising lattice model of ferromagnetic but takes deal with the social phenomenon. Set of corruption agents is considered. It is supposed ... More
Adapted Wasserstein Distances and Stability in Mathematical FinanceJan 22 2019Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility ... More
Option Pricing in Illiquid Markets with JumpsJan 19 2019The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying ... More
Conditional Optimal Stopping: A Time-Inconsistent OptimizationJan 17 2019Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent ... More
Instantaneous Arbitrage and the CAPMJan 16 2019This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation ... More
Acquisition of Project-Specific Assets with Bayesian UpdatingJan 14 2019We study the impact of learning on the optimal policy and the time-to-decision in an infinite-horizon Bayesian sequential decision model with two irreversible alternatives, exit and expansion. In our model, a firm undertakes a small-scale pilot project ... More
A Risk-Sharing Framework of Bilateral ContractsJan 12 2019We propose a risk-sharing framework for bilateral contracts to find the optimal pair, initial price and amount of collateral, with presence of default risks, collateral, and funding spreads. The derived optimal collateral can be used for contracts between ... More
On the bail-out dividend problem for spectrally negative Markov additive modelsJan 10 2019Jan 31 2019This paper studies the bail-out optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection strategy when the ... More
Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bondsJan 10 2019In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis. The results ... More
A Conjecture Involving Positive Solutions of a Simple Scalar Linear Time-Varying State Equation with DelayJan 08 2019A simple conjecture is presented concerning positive solutions of a scalar, time-varying, linear state equation with delay. Although the equation arises in the context of stock trading, no knowledge of finance is needed in the analysis to follow. Starting ... More
Evaluating betting odds and free coupons using desirabilityJan 07 2019In the UK betting market, bookmakers often offer a free coupon to new customers. These free coupons allow the customer to place extra bets, at lower risk, in combination with the usual betting odds. We are interested in whether a customer can exploit ... More
Invest or Exit? Optimal Decisions in the Face of a Declining Profit StreamJan 06 2019Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point ... More
Optimal execution with dynamic risk adjustmentJan 03 2019This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated ... More
Consumption, Investment, and Healthcare with AgingJan 02 2019Jan 07 2019This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect Gompertz' law and investment opportunities are constant. Healthcare slows ... More
Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memoryJan 02 2019Jan 07 2019In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions ... More
The robust superreplication problem: a dynamic approachDec 28 2018Feb 15 2019In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative to a family ... More
The robust superreplication problem: a dynamic approachDec 28 2018In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative to a family ... More
Predicting the Stock Price of Frontier Markets Using Modified Black-Scholes Option Pricing Model and Machine LearningDec 27 2018The Black-Scholes Option pricing model (BSOPM) has long been in use for valuation of equity options to find the prices of stocks. In this work, using BSOPM, we have come up with a comparative analytical approach and numerical technique to find the price ... More
Characterization of the Ito IntegralDec 23 2018This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to ... More
Affine Rough ModelsDec 20 2018The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential-affine transform formulas.
Closed-form expansions for option prices with respect to the mixing solutionDec 19 2018Feb 14 2019We consider closed-form expansions for European put option prices within several stochastic volatility frameworks with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing ... More
Closed-form expansions for option prices with respect to the mixing solutionDec 19 2018We consider closed-form expansions for European put option prices within several stochastic volatility frameworks with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing ... More
Network Effects and Default Clustering for Large PortfoliosDec 18 2018We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution ... More
Path Dependent Optimal Transport and Model Calibration on Exotic DerivativesDec 09 2018In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality ... More
Asymptotic Filter Behavior for High-Frequency Expert Opinions in a Market with Gaussian DriftDec 09 2018This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the ... More
The Alpha-Heston Stochastic Volatility ModelDec 05 2018We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by $\alpha$-stable processes with $\alpha\in(1,2]$. In this framework, we examine the implied volatility and its asymptotic behaviors ... More
An Optimal Extraction Problem with Price ImpactDec 04 2018A price-maker company extracts an exhaustible commodity from a reservoir, and sells it instantaneously in the spot market. In absence of any actions of the company, the commodity's spot price evolves either as a drifted Brownian motion or as an Ornstein-Uhlenbeck ... More
PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes EquationDec 03 2018Jan 18 2019The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via ... More
Optimal Transport on the Probability Simplex with Logarithmic CostNov 30 2018Motivated by the financial problem of building financial portfolios which outperform the market, Pal and Wong considered optimal transport on the probability simplex $\triangle^n$ where the cost function is induced by the free energy. We study the regularity ... More
Asymptotic distribution of capital in a model of an investment market with competitionNov 29 2018We consider a stochastic game-theoretic model of an investment market in continuous time where investors compete for dividend income from several assets. Asset prices are determined endogenously from the equality of supply and demand. The main results ... More
Uniqueness for contagious McKean--Vlasov systems in the weak feedback regimeNov 29 2018We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By weak ... More
Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costsNov 28 2018In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage ... More
Option Pricing in a Regime Switching Jump Diffusion ModelNov 28 2018Feb 05 2019This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, ... More
Swimming with Wealthy Sharks: Longevity, Volatility and the Value of Risk PoolingNov 28 2018Who {\em values} life annuities more? Is it the healthy retiree who expects to live long and might become a centenarian, or is the unhealthy retiree with a short life expectancy more likely to appreciate the pooling of longevity risk? What if the unhealthy ... More
The implied longevity curve: How long does the market think you are going to live?Nov 25 2018We use life annuity prices to extract information about human longevity using a framework that links the term structure of mortality and interest rates. We invert the model and perform nonlinear least squares to obtain implied longevity forecasts. Methodologically, ... More
Retirement spending and biological ageNov 25 2018We solve a lifecycle model in which the consumer's chronological age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in time like a broken clock that might occasionally move backwards. In ... More
Fast mean-reversion asymptotics for large portfolios of stochastic volatility modelsNov 21 2018We consider a large portfolio limit where the asset prices evolve according certain stochastic volatility models with default upon hitting a lower barrier. When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit ... More
On approximations of Value at Risk and Expected Shortfall involving kurtosisNov 15 2018We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal ... More
General Compound Hawkes Processes in Limit Order BooksNov 06 2018In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large ... More
A Stochastic Control Approach to Managed Futures PortfoliosNov 05 2018We study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity futures or ... More
Continuity of Utility Maximization under Weak ConvergenceNov 04 2018Dec 04 2018In this paper we find sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We provide several examples which illustrate ... More
Robust risk aggregation with neural networksNov 01 2018We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for ... More
Forward transition ratesOct 31 2018The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions ... More
Affine Jump-Diffusions: Stochastic Stability and Limit TheoremsOct 31 2018Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in ... More
On the solution uniqueness in portfolio optimization and risk analysisOct 26 2018Nov 01 2018We consider the issue of solution uniqueness for portfolio optimization problem and its inverse for asset returns with a finite number of possible scenarios. The risk is assessed by deviation measures introduced by [Rockafellar et al., Mathematical Programming, ... More
Term structure modeling for multiple curves with stochastic discontinuitiesOct 23 2018The goal of the paper is twofold. On the one hand, we develop the first term structure framework which takes stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the ... More
Global Closed-form Approximation of Free Boundary for Optimal Investment Stopping ProblemsOct 22 2018In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear ... More
Hyperfinite Construction of $G$-expectationOct 22 2018The hyperfinite $G$-expectation is a nonstandard discrete analogue of $G$-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time $G$-expectation operator is defined as a hyperfinite $G$-expectation which is infinitely ... More
Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing ModelsOct 22 2018We focus on two particular aspects of model risk: the inability of a chosen model to fit observed market prices at a given point in time (calibration error) and the model risk due to recalibration of model parameters (in contradiction to the model assumptions). ... More
Scaling Limits for Super--replication with Transient Price ImpactOct 17 2018We prove limit theorems for the super-replication cost of European options in a Binomial model with transient price impact. We show that if the time step goes to zero and the effective resilience between consecutive trading times remains constant then ... More
Mean-Field Games with Differing Beliefs for Algorithmic TradingOct 14 2018Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market ... More
The Broad Consequences of Narrow BankingOct 12 2018We investigate the macroeconomic consequences of narrow banking in the context of stock-flow consistent models. We begin with an extension of the Goodwin-Keen model incorporating time deposits, government bills, cash, and central bank reserves to the ... More
Classifying Markets up to IsomorphismOct 08 2018We define a notion of isomorphism for financial markets in both discrete and continuous time. We classify complete one-period markets. We define an invariant of continuous time complete markets which we call the absolute market price of risk. This invariant ... More
Dividend Policy and Capital Structure of a Defaultable FirmOct 08 2018Default risk significantly affects the corporate policies of a firm. We develop a model in which a limited liability entity subject to Poisson default shock jointly sets its dividend policy and capital structure to maximize the expected lifetime utility ... More
Exact Replication of the Best Rebalancing Rule in HindsightOct 05 2018This paper prices and replicates the financial derivative whose payoff at $T$ is the wealth that would have accrued to a $\$1$ deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the ... More
An Efficient Approach for Removing Look-ahead Bias in the Least Square Monte Carlo Algorithm: Leave-One-OutOct 04 2018The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz [2001] is the most widely used method for pricing options with early exercise features. The LSM estimator contains look-ahead bias, and the conventional technique of removing ... More
Change of Measure in the Heston Model given a violated Feller ConditionSep 28 2018When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes this gap in the ... More
Some Nontrivial Properties of a Formula for Compound InterestSep 27 2018We analyze the classical model of compound interest with a constant per-period payment and interest rate. We examine the outstanding balance function as well as the periodic payment function and show that the outstanding balance function is not generally ... More
A Numerical Study of Carr and Lee's Correlation Immunization Strategy for Volatility DerivativesSep 26 2018In their seminal work `Robust Replication of Volatility Derivatives,' Carr and Lee show how to robustly price and replicate a variety of claims written on the quadratic variation of a risky asset under the assumption that the asset's volatility process ... More
Trading Strategies Generated by Path-dependent Functionals of Market WeightsSep 26 2018Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another ... More
k-price auctions and Combination auctionsSep 26 2018Oct 15 2018We provide an exact analytical solution of the Nash equilibrium for $k$- price auctions. We also introduce a new type of auction and demonstrate that it has fair solutions other than the second price auctions, therefore paving the way for replacing second ... More
Deterministic Conditions for the Absence and Existence of Arbitrage in Continuous Financial MarketsSep 25 2018Nov 22 2018We introduce a general framework for one- and multidimensional financial markets and study no arbitrage conditions. More precisely, we derive deterministic conditions for the existence and nonexistence of equivalent (local) martingale measures and strict ... More
Robustness in the Optimization of Risk MeasuresSep 25 2018In this paper, we study issues of robustness in the context of Quantitative Risk Management. Depending on the underlying objectives, we develop a general methodology for determining whether a given risk measurement related optimization problem is robust. ... More
Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous TimeSep 24 2018Jan 22 2019A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous ... More
On a gap between rational annuitization price for producer and price for customerSep 24 2018The paper studies pricing of insurance products focusing on the pricing of annuities under uncertainty. This pricing problem is crucial for financial decision making and was studied intensively, however, many open questions still remain. In particular, ... More
Time-consistent conditional expectation under probability distortionSep 21 2018We introduce a new notion of conditional nonlinear expectation where the underlying probability scale is distorted by a weight function. Such a distorted nonlinear expectation is not sub-additive in general, so is beyond the scope of Peng's framework ... More
On the quasi-sure superhedging duality with frictionsSep 20 2018We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under portfolio constraints and model uncertainty. Frictions are modeled through solvency cones as in the original model of [Kabanov, Y., Hedging ... More
Geometric Local Variance Gamma modelSep 19 2018Dec 25 2018This paper describes another extension of the Local Variance Gamma model originally proposed by P. Carr in 2008, and then further elaborated on by Carr and Nadtochiy, 2017 (CN2017), and Carr and Itkin, 2018 (CI2018). As compared with the latest version ... More
Eventological H-theoremSep 19 2018We prove the eventological $H$-theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of thermodynamics) for what ... More
A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple TenorsSep 18 2018Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. ... More
An incomplete equilibrium with a stochastic annuitySep 16 2018We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimize their expected utility over both running consumption and terminal wealth. The market consists of a traded annuity, and, ... More
Hyperbolic normal stochastic volatility modelSep 11 2018For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two ... More
Model Risk Measurement under Wasserstein DistanceSep 11 2018The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. ... More
Model Risk Measurement under Wasserstein DistanceSep 11 2018Mar 02 2019The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. ... More
A class of stochastic games and moving free boundary problemsSep 10 2018Sep 17 2018In this paper we propose and analyze a class of stochastic $N$-player games that includes finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem, which ... More
Systemic Risk and the Dependence StructuresSep 10 2018We propose a dynamic model of dependence structure between financial institutions within a financial system and we construct measures for dependence and financial instability. Employing Markov structures of joint credit migrations, our model allows for ... More
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equationsSep 07 2018Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and computational ... More
Pricing the Aunt Michaela Option with a Modified Black-Scholes Equation with a Maturity Condition of Gamma TypeSep 06 2018Using Maple, we compute a new exact series solution of a modified Black-Scholes equation, recently proposed, for the case of the Aunt Michaela option with a maturity condition of gamma type. We show that the modified Black-Scholes equation with the Aunt ... More