Sandun Perera

A jump model for fads in asset prices under asymmetric information

This paper addresses how asymmetric information, fads and Levy jumps in the price of an asset affect the optimal portfolio strategies and maximum expected utilities of two distinct classes of rational investors in a financial market. We obtain the investors’ optimal portfolios and maximum expected logarithmic utilities and show that the optimal portfolio of each investor is more or less than its Merton optimal. Our approximation results suggest that jumps reduce the excess asymptotic utility of the informed investor relative to that of uninformed investor, and hence jump risk could be helpful for market efficiency as an indirect reducer of information asymmetry. Our study also suggests that investors should pay more attention to the overall variance of the asset pricing process when jumps exist in fads models. Moreover, if there are very little or too much fads, then the informed investor has no utility advantage in the long run.

Impulse control with random reaction periods: A central bank intervention problem

a b s t r a c t We model an impulse control problem when the controllers action affects the state as well as the dynamics of the state process for a random amount of time. We apply our model to solve a central bank intervention problem in the foreign exchange market when the market observes and reacts to the banks interventions.

Market-reaction-adjusted optimal central bank intervention policy in a forex market with jumps

Impulse control with random reaction periods (ICRRP) is used to derive a country’s optimal foreign exchange (forex) rate intervention policy when the forex market reacts to the interventions. This paper extends the previous work on ICRRP by incorporating a multi-dimensional jump diffusion process to model the state dynamics, and hence, enhance the viability of the extant model for applications. Furthermore, we employ a novel minimum cost operator that simplifies the computations of the optimal solutions. Finally, we demonstrate the efficacy of our framework by finding a market-reaction-adjusted optimal central bank intervention (CBI) policy for a country. Our numerical results suggests that market reactions and the jumps in the forex market are complements when the reactions increase the forex rate volatility; otherwise, they are substitutes.

On the existence and uniqueness of the optimal central bank intervention policy in a forex market with jumps

We study a central bank intervention (CBI) problem in the foreign exchange market when the exchange rate follows a jump-diffusion process and show that the optimal CBI policy is a control-band policy. Our main contribution is a rigorous proof of the existence and uniqueness of the optimal CBI policy.

An approximation scheme for impulse control with random reaction periods

Abstract We propose an approximation scheme for impulse control models with random reaction periods (ICRRP) and show that the optimal solutions can be found by solving a sequence of optimal stopping problems. Our work enhances viability of the existing ICRRP framework for applications as well as the general literature on stochastic control theory. The efficacy of our approximation scheme is validated by applying it to compute a market-reaction-adjusted optimal central bank intervention policy for a country.

On the sensitivity of the Black capital asset pricing model to the market portfolio

We show that Black Capital Asset Pricing Model (Black CAPM) is extremely sensitive to the choice of the market portfolio and becomes unstable as market portfolios approach the Global Minimum-Variance portfolio. When market portfolios approach the minimum-variance portfolio, the expected return on the zero beta asset approaches negative infinity and its variance increases rapidly. Moreover, expected return on a fixed portfolio becomes indefinite (i.e., takes infinitely many values), and betas of all portfolios approach one. Unlike the Sharpe-Lintner CAPM, the market risk premium in the Black CAPM always has a positive minimum, while beta may have a negative minimum value, dependent on the underlying covariance matrix.