This paper studies the mixed zero-sum stochastic differential game problem. We allow functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. show existence solution for this we prove saddle-point game. Moreover, in Markovian framework that value function unique viscosity associated Hamilton–Jacobi–Bellman (H...

We study the relative value iteration for the ergodic control problem under a nearmonotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasilinear parabolic Cauchy initial value problem in R. We show that this Cauchy problem stabilizes, or in other words, that the solution of the quasilinear parabolic equation converges f...

This study investigates the optimal switching boundary to a renewable fuel when oil prices exhibit continuous random fluctuations along with occasional discontinuous jumps. In this paper, oil prices are modeled to follow jump diffusion processes. A completeness result is derived. Given that the market is complete the value of a contingent claim is risk neutral expectation of the discounted pay ...

This paper focuses on the optimal investment problem for an insurer and a reinsurer. The insurer’s and reinsurer’s surplus processes are both approximated by a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. In addition, both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. We first study the optimiz...

This paper draws on two sources of motivation: (1) The European Union Emission Trading Scheme (EU-ETS) aims at limiting the overall emissions of greenhouse gases. The optimal abatement strategy of companies for the use of emission permits can be described as the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is a question of general interest, how regulatory constraints can b...

We consider a class of diffusions controlled through the drift and jump size, driven by Lévy process nondegenerate Wiener process, we study infinite horizon (ergodic) risk-sensitive control problems for this model. start with Dirichlet eigenvalue problem in smooth bounded domains, which also allows us to generalize current results literature on exit rate problems. Then average minimization maxi...

This paper is concerned with mean-variance portfolio selection problems in continuoustime under the constraint that short-selling of stocks is prohibited. The problem is formulated as a stochastic optimal linear-quadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take nonnegative values due to the no-shorting restr...

In this work we present a result on the non-existence of monotone, consistent linear discrete approximation of order higher than 2. This is an essential ingredient, if we want to solve numerically nonlinear and particularly Hamilton-Jacobi-Bellman (HJB) equations.

We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show that there always exists a solution to the risk-sensitive Hamilton–Jacobi–Bellman (HJB) equation, and that any minimizer in the Hamiltonian is op...

In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation which stems from the dynamic programming approach. However, the bottleneck is mainly due to the curse of dime...