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In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in…
In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment…
We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in…
We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level…
A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…
This paper studies the income fluctuation problem with capital income risk (i.e., dispersion in the rate of return to wealth). Wealth returns and labor earnings are allowed to be serially correlated and mutually dependent. Rewards can be…
We study optimal stopping for diffusion processes with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
The paper considers an investment timing problem appearing in real options theory. Present values from an investment project are modeled by general diffusion process. We prove necessary and sufficient conditions under which an optimal…
In this paper, we investigate an optimal investment problem associated with proportional portfolio insurance (PPI) strategies in the presence of jumps in the underlying dynamics. PPI strategies enable investors to mitigate downside risk…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
We consider a two-dimensional optimal dividend problem in the context of two branches of an insurance company with compound Poisson surplus processes dividing claims and premia in some specified proportions. We solve the stochastic control…
This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state…
In this paper we study a revenue maximization problem for optical routing nodes. We model the routing node as a single server polling model with the aim to assign visit periods (service windows) to the different stations (ports) such that…
This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The…
Using a combination of incentive modeling and empirical meta-analyses, this paper provides a pointed critique at the incentive systems that drive venture capital firms to optimize their practices towards activities that increase General…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…
Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each…