We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric...

The claim arrival process to an insurance company is modeled by a compound Poisson process whose intensity and/or jump size distribution changes at an unobservable time with a known distribution. It is in the insurance company’s interest to detect the change time as soon as possible in order...

In this paper we study the dividend optimization problem for a corporation or a financial institution when the management faces (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein–Uhlenbeck and square-root...

We study two practical optimization problems in relation to venture capital investments and/or Research and Development (R&D) investments. In the first problem, given the amount of the initial investment and the cash flow structure at the initial public offering (IPO), the venture capitalist...

In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator f has quadratic growth in the z-variable. In particular, we obtain existence, uniqueness, and stability results,...

We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the...

We determine how an individual can use life insurance to meet a bequest goal. We assume that the individual’s consumption is met by an income from a job, pension, life annuity, or Social Security. Then, we consider the wealth that the individual wants to devote towards heirs (separate from any...

On a filtered probability space $(\Omega,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{0\leq t\leq T})$, we consider stopper-stopper games $\bar C:=\inf_{\Rho}\sup_{\tau\in\T}\E[U(\Rho(\tau),\tau)]$ and $\underline C:=\sup_{\Tau}\inf_{\rho\in\T}\E[U(\Rho(\tau),\tau)]$ in continuous time, where...

In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for...