Related papers: Conditional Expectation expression in mean-field S…
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes…
This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic…
In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier,…
Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a stochastic differential equation…
The paper derives saddlepoint expansions for conditional expectations in the form of $\mathsf{E}[\overline{X} | \overline{\mathbf Y} = {\mathbf a}]$ and $\mathsf{E}[\overline{X} | \overline{\mathbf Y} \geq {\mathbf a}]$ for the sample mean…
We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stated as smoothness and boundedness requirements on utility…
In this paper, we are interested in conditional McKean-Vlasov jump diffusions, which are also termed as McKean-Vlasov stochastic differential equations with jump idiosyncratic noise and jump common noise. As far as conditional McKean-Vlasov…
In this paper, we investigate the optimal control problems for stochastic differential equations (SDEs in short) of mean-field type with jump processes. The control variable is allowed to enter into both diffusion and jump terms. This…
In this paper we prove the existence and uniqueness theorem, comparison theorem of a class of anticipated mean-field backward stochastic differential equations with jumps.
The paper Borovkova et al. [4] uses moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use moment matching method to obtain semi-closed form formulas…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift,…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
We study the adapted solution, numerical methods, and related convergence analysis for a unified backward stochastic partial differential equation (B-SPDE). The equation is vector-valued, whose drift and diffusion coefficients may involve…
Characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numerical computations are required to solve it. Strong efforts…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…