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The sum of log-normal variates in geometric Brownian motionFeb 08 2018Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology ... More
Collateral Unchained: Rehypothecation networks, concentration and systemic effectsFeb 06 2018We study how network structure affects the dynamics of collateral in presence of rehypothecation. We build a simple model wherein banks interact via chains of repo contracts and use their proprietary collateral or re-use the collateral obtained by other ... More
At What Frequency Should the Kelly Bettor Bet?Jan 20 2018We study the problem of optimizing the betting frequency in a dynamic game setting using Kelly's celebrated expected logarithmic growth criterion as the performance metric. The game is defined by a sequence of bets with independent and identically distributed ... More
The Stretch to Stray on Time: Resonant Length of Random Walks in a TransientJan 16 2018First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time, ... More
Robust Pricing and Hedging around the GlobeJul 26 2017We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of payoffs that includes ... More
Multiperiod Martingale TransportMar 30 2017Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called left-monotone ... More
Financial market with no riskless (safe) assetDec 07 2016We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; ... More
Stability of calibration procedures: fractals in the Black-Scholes modelDec 06 2016Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities ... More
A multi-asset investment and consumption problem with transaction costsDec 05 2016In this article we study a multi-asset version of the Merton investment and consumption problem with proportional transaction costs. In general it is difficult to make analytical progress towards a solution in such problems, but we specialise to a case ... More
Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction ApproachDec 03 2016This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an analytical ... More
How many market makers does a market need?Dec 03 2016We consider a simple model for the evolution of a limit order book in which limit orders of unit size arrive according to independent Poisson processes. The frequency of buy limit orders below a given price level, respectively sell limit orders above ... More
Optimal consumption and investment under transaction costsDec 02 2016In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation, and find that ... More
Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolioNov 29 2016Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact that this result ... More
Portfolio optimization near horizonNov 28 2016Portfolio optimization is a well-known problem in mathematical finance concerned with selecting a portfolio which will maximize the expected terminal utility of an investor given today's information and subject to some constraints. It has been studied ... More
Generalization of Doob Decomposition Theorem and Risk Assessment in Incomplete MarketsNov 28 2016In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This Theorem is a generalization ... More
Dynamical Stationarity as a Result of Sustained Random GrowthNov 21 2016In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master ... More
Systemic Risk and Interbank LendingNov 21 2016We propose a simple model of inter-bank lending and borrowing incorporating a game feature where the evolution of monetary reserve is described by a system of coupled Feller diffusions. The optimization subject to the quadratic cost reflects the desire ... More
On convex functions on the duals of $Δ_2$-Orlicz spacesNov 18 2016In the dual $L^{\Phi^*}$ of a $\Delta_2$-Orlicz space $L^\Phi$, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology $\tau(L^{\Phi^*},L^\Phi)$ if and only if on each order interval $[-\zeta,\zeta]=\{\xi: ... More
Robust Trading of Implied SkewNov 17 2016In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the validity of a specific ... More
Computation of first-order Greeks for barrier options using chain rules for Wiener path integralsNov 16 2016This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain ... More
Predictable Forward Performance Processes: The Binomial CaseNov 14 2016We introduce a new class of forward performance processes that are predictable with regards to an underlying filtration and are updated in discrete time. Such performance criteria may accommodate short-term predictability of asset returns, sequential ... More
On the wavelets-based SWIFT method for backward stochastic differential equationsNov 09 2016We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting ... More
Unexpected Default in an Information Based ModelNov 09 2016This paper provides sufficient conditions for the time of bankruptcy (of a company or a state) for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information ... More
Disentangling wrong-way risk: pricing CVA via change of measures and drift adjustmentNov 09 2016A key driver of Credit Value Adjustment (CVA) is the possible dependency between exposure and counterparty credit risk, known as Wrong-Way Risk (WWR). At this time, addressing WWR in a both sound and tractable way remains challenging: arbitrage-free setups ... More
Pricing Derivatives in a Regime Switching Market with Time Inhomogeneous VolatilityNov 07 2016This paper studies pricing derivatives in an age-dependent semi-Markov modulated market. We consider a financial market where the asset price dynamics follow a regime switching geometric Brownian motion model in which the coefficients depend on finitely ... More
`To Have What They are Having': Portfolio Choice for Mimicking Mean-Variance SaversNov 04 2016We consider a group of mean-variance investors with mimicking desire such that each investor is willing to penalize deviations of his portfolio composition from compositions of other group members. Penalizing norm constraints are already applied for statistical ... More
Liquidity induced asset bubbles via flows of ELMMsNov 04 2016We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in the work of Jarrow, Protter and Roch (2012). ... More
Liquidity induced asset bubbles via flows of ELMMsNov 04 2016Nov 24 2016We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in the work of Jarrow, Protter and Roch (2012). ... More
An Axiomatization of Naive DiversificationNov 04 2016A widely applied diversification paradigm is the naive diversification choice heuristic. It stipulates that an economic agent allocates equal decision weights to given choice alternatives independent of their individual characteristics. This article provides ... More
Naive Diversification Preferences and their RepresentationNov 04 2016Nov 09 2016A widely applied diversification paradigm is the naive diversification choice heuristic. It stipulates that an economic agent allocates equal decision weights to given choice alternatives independent of their individual characteristics. This article provides ... More
Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility FunctionNov 03 2016We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option priceWe investigate qualitative and quantitative behavior of a solution to the problem of pricing ... More
Pricing Bounds for VIX Derivatives via Least Squares Monte CarloNov 02 2016Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed ... More
Option pricing in exponential Lévy models with transaction costsNov 01 2016We present an approach for pricing a European call option in presence of proportional transaction costs, when the stock price follows a general exponential L\'evy process. The model is a generalization of the celebrated work of Davis, Panas and Zariphopoulou ... More
Option pricing in exponential Lévy models with transaction costsNov 01 2016Nov 21 2016We present an approach for pricing a European call option in presence of proportional transaction costs, when the stock price follows a general exponential L\'{e}vy process. The model is a generalization of the celebrated work of Davis, Panas and Zariphopoulou ... More
Option pricing in exponential Lévy models with transaction costsNov 01 2016Nov 30 2016We present an approach for pricing a European call option in presence of proportional transaction costs, when the stock price follows a general exponential L\'evy process. The model is a generalization of the celebrated work of Davis, Panas and Zariphopoulou ... More
Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type ContractsOct 31 2016Catastrophe risk is a major threat faced by individuals, companies, and entire economies. Catastrophe (CAT) bonds have emerged as a method to offset this risk and a corresponding literature has developed that attempts to provide a market-consistent pricing ... More
Equitable retirement income tontines: Mixing cohorts without discriminatingOct 28 2016There is growing interest in the design of pension annuities that insure against idiosyncratic longevity risk while pooling and sharing systematic risk. This is partially motivated by the desire to reduce capital and reserve requirements while retaining ... More
Optimal retirement income tontinesOct 28 2016Tontines were once a popular type of mortality-linked investment pool. They promised enormous rewards to the last survivors at the expense of those died early. And, while this design appealed to the gambling instinc}, it is a suboptimal way to generate ... More
Calls, zonoids, peacocks and log-concavityOct 28 2016The main results are two characterisations of log-concave densities in terms of the collection of lift zonoids corresponding to a peacock. These notions are recalled and connected to arbitrage-free asset pricing in financial mathematics.
Super-Replication with Fixed Transaction CostsOct 28 2016We study super-replication of contingent claims in markets with fixed transaction costs. The first result in this paper reveals that in reasonable continuous time financial market the super--replication price is prohibitively costly and leads to trivial ... More
Robust Utility Maximization in Discrete-Time Markets with FrictionOct 28 2016We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial ... More
Model-independent pricing with insider information: a Skorokhod embedding approachOct 28 2016In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling assumptions, but ... More
Optimal Extraction and Taxation of Strategic Natural Resources: A Differential Game ApproachOct 27 2016This paper studies the optimal extraction and taxation of nonrenewable natural resources. It is well known the market values of the main strategic resources such as oil, natural gas, uranium, copper,...,etc, fluctuate randomly following global and seasonal ... More
The dual representation problem of risk measuresOct 27 2016The objective of this paper is to present a comprehensive study of the dual representation problem of risk measures and convex functionals on a Banach lattice $X$. Of particular interest is the case where $X$ is an Orlicz space or an Orlicz heart. The ... More
Intrinsic risk measuresOct 27 2016Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach provides a direct ... More
Utility Maximization and Indifference Value under Risk and Information Constraints for a Market with a Change PointOct 27 2016In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset ... More
Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price DynamicsOct 26 2016This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric Brownian motion and ... More
Approximate pricing of European and Barrier claims in a local-stochastic volatility settingOct 18 2016We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation ... More
An explicit formula for optimal portfolios in complete Wiener driven markets: a functional Itô calculus approachOct 17 2016The optimal investment problem is one of the most important problems in mathematical finance. The main contribution of the present paper is an explicit formula for the optimal portfolio process. Our optimal investment problem is that of maximizing the ... More
The Fatou Property under Model UncertaintyOct 13 2016We provide a characterization in terms of Fatou property for weakly closed monotone sets in the space of $\Pcal$-quasisure bounded random variables, where $\Pcal$ is a (possibly non-dominated) class of probability measures. Our results can be applied ... More
The Fatou Property under Model UncertaintyOct 13 2016Nov 02 2016We provide a characterization in terms of Fatou closedness for weakly closed monotone sets in the space of $\Pcal$-quasisure bounded random variables, where $\Pcal$ is a (possibly non-dominated) class of probability measures. Our results can be applied ... More
Time value of extra information against its timely valueOct 13 2016We introduce an interactive market setup with sequential auctions where agents receive variegated signals with a known deadline. The effects of differential information and mutual learning on the allocation of overall profit \& loss (P\&L) and the pace ... More
On Origins of BubblesOct 12 2016We discuss - in what is intended to be a pedagogical fashion - a criterion, which is a lower bound on a certain ratio, for when a stock (or a similar instrument) is not a good investment in the long term, which can happen even if the expected return is ... More
Barrier Option Pricing under the 2-Hypergeometric Stochastic Volatility ModelOct 11 2016Aug 03 2017We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation ... More
Barrier Option Pricing under the 2-Hypergeometric Stochastic Volatility ModelOct 11 2016The purpose of this work is to investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model which has recently been introduced as an attempt to tackle one of the most serious ... More
Option pricing with Legendre polynomialsOct 10 2016Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density function rapidly ... More
Dependent Defaults and Losses with Factor Copula ModelsOct 10 2016We introduce a class of flexible and tractable static factor models for the joint term structure of default probabilities, the factor copula models. These high dimensional models remain parsimonious with pair copula constructions, and nest numerous standard ... More
Constrained Optimal TransportOct 10 2016The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\cal ... More
Volatility Smile as Relativistic EffectOct 08 2016We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution 1) is properly normalized and 2) obeys the tower law (semigroup property), so we can construct martingales and self-financing ... More
Trading against disorderly liquidation of a large position under asymmetric information and market impactOct 06 2016We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price ... More
Mixture Diffusion for Asset PricingOct 05 2016Oct 12 2016This paper proposes a general form of mixture diffusion process to model asset price dynamics, using a mixture of infinite number of parametric diffusions. We show that the underlying asset price dynamics of the risk-neutral probability density distributions ... More
Mixture Diffusion for Asset PricingOct 05 2016Oct 30 2016This paper proposes a general form of mixture diffusion process to model asset price dynamics, using a mixture of infinite number of parametric diffusions. We show that the underlying asset price dynamics of the risk-neutral distributions can be modeled ... More
A Duality Result for Robust Optimization with Expectation ConstraintsOct 04 2016This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial derivatives. ... More
The Long Bond, Long Forward Measure and Long-Term Factorization in Heath-Jarrow-Morton ModelsOct 04 2016This paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the function space ... More
Long-Term Factorization of Affine Pricing KernelsOct 03 2016This paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. ... More
Optimal Portfolios of Illiquid AssetsOct 03 2016This paper investigates the investment behaviour of a large unregulated financial institution (FI) with CARA risk preferences. It shows how the FI optimizes its trading to account for market illiquidity using an extension of the Almgren-Chriss market ... More
Decoupling the short- and long-term behavior of stochastic volatilityOct 02 2016We study the empirical properties of realized volatility of the E-mini S&P 500 futures contract at various time scales, ranging from a few minutes to one day. Our main finding is that intraday volatility is remarkably rough and persistent. What is more, ... More
Volatility Inference and Return Dependencies in Stochastic Volatility ModelsOct 02 2016Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock returns can be inferred ... More
Robust Optimal Investment in Discrete Time for Unbounded Utility FunctionSep 29 2016Oct 04 2016This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with measurable selection ... More
Strongly Consistent Multivariate Conditional Risk MeasuresSep 26 2016We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced ... More
Data-driven nonlinear expectations for statistical uncertainty in decisionsSep 21 2016In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently ... More
Bounds for VIX Futures given S&P 500 SmilesSep 19 2016We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting ... More
The microstructural foundations of leverage effect and rough volatilitySep 16 2016We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in this model ... More
Asset Pricing in a Semi-Markov Modulated Market with Time-dependent VolatilitySep 15 2016This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models ... More
Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimizationSep 13 2016Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk ... More
Canonical Supermartingale CouplingsSep 09 2016Nov 26 2017Two probability distributions $\mu$ and $\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich ... More
Canonical Supermartingale CouplingsSep 09 2016Two probability distributions $\mu$ and $\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich ... More
A superhedging approach to stochastic integrationSep 08 2016Using Vovk's outer measure, which corresponds to a minimal superhedging price, the existence of quadratic variation is shown for "typical price paths" in the space of non-negative c\`adl\`ag functions. In particular, this implies the existence of quadratic ... More
The characteristic function of rough Heston modelsSep 07 2016It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. ... More
Criteria for the Absense and Existence of Arbitrage in Multidimensional Diffusion ModelsSep 06 2016We derive abstract as well as deterministic conditions for the absence and existence of free lunch with vanishing risk, arbitrage, generalized arbitrage, and unbounded profit with bounded risk in a general multidimensional diffusion framework. Moreover, ... More
Criteria for the Absence and Existence of Arbitrage in Multi- and Infinite-Dimensional Diffusion MarketsSep 06 2016Nov 07 2016We derive abstract as well as deterministic conditions for the absence and existence of arbitrage and financial bubbles in a general (multi- and infinite-dimensional) semimartingale-diffusion markets, and a Heath-Jarrow-Morton-Musiela framework. We also ... More
Option-Based Pricing of Wrong Way Risk for CVASep 03 2016Oct 02 2016The two main issues for managing wrong way risk (WWR) for the credit valuation adjustment (CVA, i.e. WW-CVA) are calibration and hedging. Hence we start from a novel model-free worst-case approach based on static hedging of counterparty exposure with ... More
Numerical solution of a semilinear parabolic degenerate Hamilton-Jacobi-Bellman equation with singularitySep 02 2016Sep 22 2016We consider a semilinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity which is related to a stochastic control problem with fuel constraint. The fuel constraint translates into a singular initial condition for the HJB ... More
Short-Time Expansions for Call Options on Leveraged ETFs Under Exponential Lévy models With Local VolatilityAug 28 2016In this article, we consider the small-time asymptotics of options on a Leveraged Exchange-Traded Fund (LETF) when the underlying Exchange Traded Fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. Our main results ... More
Short-Time Expansions for Call Options on Leveraged ETFs Under Exponential Lévy models With Local VolatilityAug 28 2016Oct 27 2016In this article, we consider the small-time asymptotics of options on a \emph{Leveraged Exchange-Traded Fund} (LETF) when the underlying Exchange Traded Fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. Our main ... More
On the hedging strategies for defaultable claims under incomplete informationAug 25 2016In this paper we investigate the hedging problem of a defaultable claim with recovery at default time via the local risk-minimization approach when investors have a restricted information on the market. We assume that the stock price process dynamics ... More
Lévy-Vasicek Models and the Long-Bond Return ProcessAug 23 2016Sep 13 2016The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the L\'evy-Vasicek ... More
Volatility and ArbitrageAug 22 2016The capitalization-weighted total relative variation $\sum_{i=1}^d \int_0^\cdot \mu_i (t) \mathrm{d} \langle \log \mu_i \rangle (t)$ in an equity market consisting of a fixed number $d$ of assets with capitalization weights $\mu_i (\cdot)$ is an observable ... More
Optimal Switching under Ambiguity and Its Applications in FinanceAug 22 2016In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and ... More
A String Model of Liquidity in Financial MarketsAug 21 2016We consider a dynamic market model where buyers and sellers submit limit orders. If at a given moment in time, the buyer is unable to complete his entire order due to the shortage of sell orders at the required limit price, the unmatched part of the order ... More
Stochastic Evolution Equations in Banach Spaces and Applications to Heath-Jarrow-Morton-Musiela EquationAug 20 2016In this paper we study the stochastic evolution equation (1.1) in martingale-type 2 Banach spaces (with the linear part of the drift being only a generator of a C0-semigroup). We prove the existence and the uniqueness of solutions to this equation. We ... More
Consistency of option prices under bid-ask spreadsAug 19 2016Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a bid-ask spread. ... More
Filling the gaps smoothlyAug 18 2016The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the approach proposed ... More
Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian MotionAug 16 2016We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional predictability ... More
A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivativesAug 11 2016Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial ... More
Another example of duality between game-theoretic and measure-theoretic probabilityAug 09 2016This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic expectation for ... More
A time of ruin constrained optimal dividend problem for spectrally one-sided Lévy processesAug 08 2016We consider the dividends problem for both de Finetti's and Dual models for spectrally one-sided L\'evy processes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness condition in both models ... More
Who would invest only in the risk-free asset?Aug 08 2016Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa-Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor's priors there ... More
Allocation of risk capital in a cost cooperative game induced by a modified Expected ShortfallAug 08 2016The standard theory of coherent risk measures fails to consider individual institutions as part of a system which might itself experience instability and spread new sources of risk to the market participants. In compliance with an approach adopted by ... More
Arbitrage and utility maximization in market models with an insiderAug 06 2016We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses from the beginning an additional information in the form of a random variable G, which only becomes ... More