Term structure models have attracted tremendous amount of attention in the last two decades. My first paper specifies the dynamic and cross-sectional behavior of bonds in the framework of the Linear or general affine term structure model (ATSM). After revisiting the basic theory of ATSM under...

This paper studies dynamical and cross-sectional structures of bonds, typically used as riskfreeassets in mathematical finance. After reviewing a mathematical theory on commonfactors, also known as principal components, we compute empirical common factors for 10US government bonds (3month,...

This paper studies dynamical and cross-sectional structures of bonds, typically used as riskfree assets in mathematical finance. After reviewing a mathematical theory on common factors, also known as principal components, we compute empirical common factors for 10 US government bonds (3month,...

We consider the optimal consumption and investment with transaction costs on multiple assets, where the prices of risky assets jointly follow a multi-dimensional geometric Brownian motion. We characterize the optimal investment strategy and in particular prove by rigorous mathematical analysis...

We consider the Merton problem with capital gain taxes. Since closed-form solutions are generally unavailable, we provide asymptotic expansions with small interest rate and other parameters, and then obtain an explicit investment and consumption strategy that effectively approximates the optimal...

We consider a long-term portfolio choice problem with two illiquid and correlated assets and formulate it as an eigenvalue problem in the form of a variational inequality. The eigenvalue is associated with the portfolio’s optimal long-term growth rate, and the free boundaries implied by the...

In this paper, we derive a parabolic variational inequality with double time-like variables from a continuous exercise model of American call options proposed in Rogers and Schienkman (2007). Using viscosity approach, we prove that the value function is a unique viscosity solution to the...

Many finance problems can be formulated as a singular stochastic control problem, where the associated Hamilton-Jacobi-Bellman (HJB) equation takes the form of variational inequality and its penalty approximation equation is linked to a regular control problem. The penalty method, as a finite...