We consider the classical Cramér-Lundberg model with dynamic proportional reinsurance and solve the problem of finding the optimal reinsurance strategy which minimizes the expected quadratic distance of the risk reserve to a given benchmark. This result is extended to a mean-variance problem....

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism...

In this paper, we propose an efficient algorithm for a Hamilton–Jacobi–Bellman equation governing a class of optimal feedback control and stochastic control problems. This algorithm is based on a non-overlapping domain decomposition method and an adaptive least-squares collocation radial...

The paper introduces special options such that the holder selects dynamically a continuous time process controlling the distribution of the payments (benefits) over time. For instance, the holder can select dynamically the quantity of a commodity purchased or sold by a fixed price given...

We study the problem of the optimal pricing and hedging of a European option written on an illiquid asset Z using a set of proxies: a liquid asset S, and N liquid European options Pi, each written on a liquid asset Yi, i = 1, N. We assume that the S-hedge is dynamic while the multi-name Y-hedge...

In this paper, we consider a portfolio optimization problem in a defaultable market. The representative investor dynamically allocates his or her wealth among the following securities: a perpetual defaultable bond, a money market account and a default-free risky asset. The optimal investment and...

A portfolio selection problem in which the prices of stocks follow jump-diffusion process is studied. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. A stochastic linear-quadratic control problem is introduced as auxiliary problem of...

We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share...

We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the...