Related papers: Pricing approximations and error estimates for loc…

We shall study backward stochastic differential equations and we will present a new approach for the existence of the solution. This type of equation appears very often in the valuation of financial derivatives in complete markets.…

The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differential equations (BSDEs) with a random horizon in a…

We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…

A comparison principle for stochastic integro-differential equations driven by Levy processes is proved. This result is obtained via an extension of an Ito formula from [11] for the square of the norm of the positive part of $L_2-$valued,…

We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a L\'{e}vy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent L\'{e}vy measure, local…

We 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…

We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model…

We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable…

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…

We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…

We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential L\'evy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional…

We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral…

We consider the problem of determining the L\'evy exponent in a L\'evy model for asset prices given the price data of derivatives. The model, formulated under the real-world measure $\mathbb P$, consists of a pricing kernel…

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators…

We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a…

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…

We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…

A three-dimensional extension of the structural default model with firms' values driven by correlated diffusion processes is presented. Green's function based semi-analytical methods for solving the forward calibration problem and backward…

Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…