Winston S. Buckley

A mispricing model of stocks under asymmetric information

We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean-reverting Ornstein–Uhlenbeck process. Optimal portfolios and maximum expected log-linear utilities from terminal wealth for informed and uninformed investors are derived. We obtain analogous but more general results which nests those of Guasoni (2006) as a special case of the relative risk aversion approaching one.

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.

A discontinuous mispricing model under asymmetric information

We study a discontinuous mispricing model of a risky asset under asymmetric information where jumps in the asset price and mispricing are modelled by Levy processes. By contracting the filtration of the informed investor, we obtain optimal portfolios and maximum expected utilities for the informed and uninformed investors. We also discuss their asymptotic properties, which can be estimated using the instantaneous centralized moments of return. We find that optimal and asymptotic utilities are increased due to jumps in mispricing for the uninformed investor but the informed investor still has excess utility, provided there is not too little or too much mispricing.

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.

Experience Rating with Poisson Mixtures

Abstract We propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

Numerical approximations of optimal portfolios in mispriced asymmetric Lévy markets

We present numerical approximations of optimal portfolios in mispriced Levy markets under asymmetric information for informed and uninformed investors having logarithmic preference. We apply our numerical scheme to Kou (2002) jump-diffusion markets by deriving analytic formulas for the first two derivatives of the underlying portfolio objective function which depend only on the Levy measure of the jump-generating process. Optimal portfolios are then simulated using the Box–Muller algorithm, Newton’s method and incomplete Beta functions. Convergence dynamics and trajectories of sample paths of optimal portfolios for both investors are presented at different levels of information asymmetry, mispricing, horizon, asymmetry in the Kou density, jump intensity, volatility, mean-reversion speed, and Sharpe ratios. We also apply the proposed Newton’s algorithm to compute optimal portfolios for investors in Variance Gamma markets via instantaneous centralized moments of returns.

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.

The long-run excess optimal power utility of an informed investor and its approximation

We derive the mean, variances and variance bounds of optimal portfolios of informed and uninformed investors having power preference as presented in Buckley et al. (2012). In contrast, we give direct (non-log-linear) alternative representations of the optimal expected utilities and excess optimal utility of the informed investor in the long-run. We also present a new approximation for the excess optimal utility of the informed investor when the relative risk aversion is close to 1. Our approximation of the excess utility is slightly larger but nests that which is presented in prior studies.

Teaching Software Testing using Data Structures

Software testing is typically a rushed and neglected activity that is done at the final stages of software development. In particular, most students tend to test their programs manually and very seldom perform adequate testing. In this paper, two basic data structures are utilized to highlight the importance of writing effective test cases by testing their fundamental properties. The paper also includes performance testing at the unit level, of a classic recursive problem called the Towers of Hanoi. This teaching approach accomplishes two important pedagogical objectives: (1) it allows students to think about how to find hidden bugs and defects in their programs and (2) it encourages them to test more effectively by leveraging data structures that are already familiar to them.

An application of Markov chain Monte Carlo (MCMC) to continuous-time incurred but not yet reported (IBNYR) events

Abstract We develop a Bayesian model for continuous-time incurred but not yet reported (IBNYR) events under four types of secondary data, and show that unreported events, such as claims, have a Poisson distribution with a reduced arrival parameter if event arrivals are Poisson distributed. Using insurance claims as an example of an IBNYR event, we apply Markov chain Monte Carlo (MCMC) to the continuous-time IBNYR claims model of Jewell using Type I and Type IV data. We illustrate the relative stability of the MCMC method versus the Gammoid approximation of Jewell by showing that the MCMC estimates approach their prior parameters, while the Gammoid approximations grow without bound for Type IV data. Moreover, this holds for any distribution that the delay parameter is assumed to follow. Our framework also allows for the computation of posterior confidence intervals for the parameters.