We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in the binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated...

Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and examine their behavior for risk positions of long...

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the dynamics of the underlying stocks depends on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the...

In an incomplete market, with incompleteness stemming from stochas- tic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) for- ward performance processes in factor-form using ergodic BSDE. We also develop a...

This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to intertemporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitting method, whose convergence is proved based...

This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint,...