In this paper, a type of fuzzy system structure is applied to heuristic dynamic programming (HDP) algorithm to solve nonlinear discrete-time Hamilton–Jacobi–Bellman (DT-HJB) problems. The fuzzy system here is adopted as a 0-order T–S fuzzy system using triangle membership functions (MFs). The convergence of HDP and approximability of the multivariate 0-order T–S fuzzy system is analyzed in this...

We give a short introduction to the stochastic calculus for ItôLévy processes and review briefly the two main methods of optimal control of systems described by such processes: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated backward stochastic differential equation (BSDE). The two methods are illustrated by applica...

We develop a dynamic optimization framework to assess the impact of funding costs on credit swap investments. A defaultable investor can purchase CDS upfronts, borrow at a rate depending on her credit quality, and invest in the money market account. By viewing the concave drift of the wealth process as a continuous function of admissible strategies, we characterize the optimal strategy in terms...

We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper. The adverse player (nature) chooses open-loop controls that represent the so-called Knightian uncertainty, i.e., misspecifications of the model. The (half) ...

This study determined whether phosphodiesterase (PDE) was activated by protein kinase C (PKC) upon kappa-receptor stimulation, and if so, to identify the isozyme. We first studied the effects of trans-(+/-)-3,4-dichloro-N-methyl-N-(2-[1-pyrrolidinyl] cyclohexyl) benzeneacetamide methanesulphonate (U50,488H), a selective kappa-opioid receptor (OR) agonist, and phorbol-12-myristate-13-acetate (PM...

We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a nonstandard class of switching controls introduced in this paper. The adverse player (nature) chooses open-loop controls that represent the so-called Knightian uncertainty, i.e., misspecifications of the model. The (half) g...

This paper considers a class of optimization problems arising in wireless communication systems. We analyze the optimal control and the associated Hamilton–Jacobi–Bellman (HJB) equations. It turns out that the value function is a unique viscosity solution of the HJB equation in a certain function class. To deal with the fast growth condition of the value function in establishing uniqueness, we ...

We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this repor...

In this paper we consider the optimal control problem for a insurance company. Our objective is to maximize the expectation of discounted dividends and its terminal value which represents the company liquidation value upon the time of bankruptcy. The surplus of the insurance company is governed by the Brownian motion with a constant drift and a diffusion term. The company can manage its risk ex...

We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky asset. Using stochastic control, we characterize the value function as the unique classical solution of an associated Hamilton-Jacobi-Bellman (HJB) equation, obta...