This paper considers the optimal asset allocation strategy for bank with stochastic interest rates when there are three types of asset: Bank account, loans and securities. The asset allocation problem is to maximize the expected utility from terminal wealth of a bank's shareholders over a finite...

We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice continuously differentiable, as long as the control space is compact and the volatility is uniformly bounded below, away from zero. Under...

We propose the use of a mean quadratic variation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian...

We give an explicit expression for the optimal investment strategy, under the constant elasticity of variance (CEV) model, which maximizes the expected HARA utility of the final value of the surplus at the maturity time. To do this, the corresponding HJB equation will be transformed into a...

This paper investigates the optimal dividend problem of an insurance company, which controls risk exposure by reinsurance and by issuing new equity to protect from bankruptcy. Transaction costs are incurred by these business activities: reinsurance is non-cheap, dividend is taxed and fixed costs...

This paper considers the optimal dividend problem with proportional reinsurance and capital injection for a large insurance portfolio. In particular, the reinsurance premium is assumed to be calculated via the variance principle instead of the expected value principle. Our objective is to...

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...

A market portfolio plays an important role in many financial theories and models. It is at the heart of the capital asset pricing model and other multivariate models. Because of the market portfolio cannot be observed directly, proxy portfolios must be used to conduct empirical studies....

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...