In this paper, in a time-homogeneous diffusion setting, we study a sequence of last passage times of generalized drawdown processes before the first passage time of another monitoring generalized drawdown process. These quantities are closely related to consecutive small market downward...

In this paper, we propose an efficient approach to the calculation of risk measures for an insurer's liability from writing a variable annuity with guaranteed benefits. Our approach is based on a novel application of the Hermite series expansions on the transition density of a diffusion process...

In this paper, we propose a theoretical and computational framework for the detection and identification of (triangular) arbitrage opportunities among spot currency exchange rates in a foreign exchange market. We obtain sufficient conditions for excluding the triangular arbitrage opportunities...

We obtain exact semi-explicit solutions to the optimal pricing problem for the multinomial logit (MNL) consumer choice model with network effects, through a novel conditioning argument and the use of the Lambert W function. Then we manage to characterize the exact optimal solution in the...

We present a general purpose technique for the efficient and accurate valuation of options in the shifted Stochastic Alpha Beta Rho (shifted-SABR) model which includes SABR as a special case. The method is based on a novel double-layer continuous-time Markov chain (CTMC) from which closed-form...

We establish a novel duality relationship between continuous and discrete non-negative additive functionals of stochastic (not necessarily Markovian) processes and their right inverses. For general Markov processes, we further extend and develop a theoretical and computational framework for the...

We study a Bayesian learning model with heterogeneity in which the agents control both short-term manipulations and long-term efforts aimed at solving the optimal contract in dynamic environments. At the same time, considering the dynamic characteristics of contracts, the paper considers the...

In this paper we study the Omega risk model with surplus-dependent tax payments in a time-homogeneous diffusion setting. The new model incorporates practical features from both the Omega risk model(Albrecher and Gerber and Shiu (2011)) and the risk model with tax(Albrecher and Hipp (2007)). We...

We consider a general framework of optimal contract design under the heterogeneity and short-termism of agents. Our research shows that the optimal contract must weigh the agent's information rent, incentive cost, and benefit to overcome the contract's adverse selection and moral hazards. Agents...