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We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth. Based on the work [9] with an additional stochastic payoff function, we characterize the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equation (BSDE for short) with unbounded terminal condition. In regard to discrete problem, we get the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provide some useful prior estimates about the solutions with the help of auxiliary forward-backward SDE system and Malliavin calculus. Finally, we obtain the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.
This paper studies an optimal investment problem under M-CEV with power utility function. Using Laplace transform we obtain explicit expression for optimal strategy in terms of confluent hypergeometric functions. For obtained representations we deriv
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic op
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly different from
We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expec
We examine Kreps (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that approach the BSM economy in a natural sense: