Abstract In this paper, we consider the stochastic optimal control problem for jump-diffusion models with state constraints. general, value function of such problems is discontinuous viscosity solution associated Hamilton-Jacobi-Bellman (HJB) equation since regularity cannot be guaranteed at boundary constraint. By adapting target theory, obtain an equivalent representation original by means ba...

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using ...

This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation and establish a functional c...

We propose a general framework for studying statistics of jump-diffusion systems driven by both Brownian noise (diffusion) and a jump process with state-dependent intensity. Of particular natural interest in many physical systems are the jump locations: the system evaluated at the jump times. As an example, this could be the voltage at which a neuron fires, or the so-called ‘threshold voltage’....

We consider the dynamic portfolio choice problem in a jump-diffusion model, where an investor may face constraints on her portfolio weights: for instance, no-short-selling constraints. It is a daunting task to use standard numerical methods to solve a constrained portfolio choice problem, especially when there is a large number of state variables. By suitably embedding the constrained problem i...

In this paper, we consider exponential Runge-Kutta methods for the numerical pricing of options. The methods are shown to be an alternative to other existing procedures for the numerical valuation of jump -diffusion models. We show that exponential Runge-Kutta methods give unconditional second order accuracy for European call options under Merton's jump -diffusion model with constant coefficien...

Many examples of complex systems are provided by applications in finance and economics areas. Some of intrinsic features of such systems lie with the fact that their parts are interacting in a non-trivial dynamic manner and they can be subject to stochastic forces and jumps. The mathematical models for such systems are often based on stochastic differential equations and efficient computational...