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...

Basel II banking regulation introduces new needs for computational schemes. They involve both optimal stochastic control, and large scale simulations of decision processes of preventing low-frequency high loss-impact events. This paper will first state the problem and present its parameters. It...

We determine the optimal dynamic investment policy for a mean quadratic variation objective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We compare the efficient frontiers and optimal investment policies for three mean variance...

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...

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....

This paper seeks to highlight two approaches to the solution of stochastic control and optimal stopping problems in continuous time. Each approach transforms the stochastic problem into a deterministic problem. Dynamic programming is a well-established technique that obtains a partial/ordinary...

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...