Vector-valued coherent risk measures

We define (d,n)-coherent risk measures as set-valued maps from into satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from valued random portfolio to valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.Received: February 2004, Mathematics Subject Classification (2000): 91B30, 46E30JEL Classification: D81, G31     

Asymptotic analysis for optimal investment and consumption with transaction costs

We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost . The utility function is of the form U(c) = c^1-p/(1-p) for p > 0, . We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of , and we also obtain asymptotic results on the boundary of the no-trade region.Received: July 2003, Mathematics Subject Classification (1991): 90A09, 60H30, 60G44JEL Classification: G13Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.     

Satisfying convex risk limits by trading

A random variable, representing the final position of a trading strategy, is deemed acceptable if under each of a variety of probability measures its expectation dominates a floor associated with the measure. The set of random variables representing pre-final positions from which it is possible to trade to final acceptability is characterized. In particular, the set of initial capitals from which one can trade to final acceptability is shown to be a closed half-line . Methods for computing are provided, and the application of these ideas to derivative security pricing is developed.Received: May 2004, Mathematics Subject Classification (2000): 91B30, 60H30, 60G44JEL Classification: G10Steven E. Shreve: Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.Reha Tütüncü: Work supported by National Science Foundation under grants CCR-9875559 and DMS-0139911.     

Robust utility maximization for complete and incomplete market models

We investigate the problem of maximizing the robust utility functional . We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques developed for f-divergences. This is a suitable tool to reduce the robust problem to the classical problem of utility maximization under a certain measure: the reverse f-projection. Furthermore, we give the dual characterization for a closely related problem, the minimization of expenditures given a minimum level of expected utility in a robust setting and for an incomplete market.Received: September 2004, Mathematics Subject Classification (2000): 62C20, 62O05, 91B16, 91B28JEL Classification: D81, G11I thank Hans Föllmer for his help when writing this paper. Furthermore, I thank Alexander Schied for discussing the topic with me and Michael Kupper and the referees for their helpful remarks.     

On the pricing of forward starting options in Heston’s model on stochastic volatility

We consider the problem of pricing European forward starting options in the presence of stochastic volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution within Hestons stochastic volatility framework applying distribution properties of the volatility process. In this paper we develop a new and more suitable formula for pricing forward starting options. This formula allows to cover the smile effects observed in a Black-Scholes environment, in which the extreme exposure of forward starting options to volatility changes is ignored.Received: July 2004, Mathematics Subject Classification (2000): 91B28, 60G44, 60H30, 60E10JEL Classification: G13It is a pleasure to thank the anonymous referee for his valuable comments and suggestions on this paper. Furthermore, we would like to thank Holger Kraft, University of Kaiserslautern, and Alexander Giese, HypoVereinsbank AG Munich, for fruitful discussions and suggestions.     

Experimental evidence of how prior experience as an auditor influences managers’ strategic reporting decisions

We design an experiment to examine the influence of audit experience on subsequent reporting decisions when auditors become managers of audited firms. In contrast to the independence issues that can arise when auditors and their clients are related by prior affiliation, we focus this study on the more common case in which auditors assume subsequent employment with other firms’ clients. In a bi-matrix experimental game that captures key features of the strategic tension between auditors and reporters, we find that reporters who have prior experience as an auditor, particularly the experience of having been a diligent auditor, are more sensitive to large penalties for aggressive reporting than are reporters whose experience is exclusively as a reporter. Our results suggest implications for regulators in predicting the effects of reporting penalties and for firms in considering the effects of CPA experience when hiring for reporting positions.

The Role of Analysts’ Forecasts in Accounting-Based Valuation: A Critical Evaluation

This paper critically evaluates the use of analysts forecasts in accounting-based valuation. Specifically, I assess the usefulness and the limitation of analysts forecasts in predicting future earnings and in explaining the market-to-book ratio, in light of a comprehensive set of 22 explicit information items, including: economic rent proxies, conservative accounting proxies, earnings quality signals, transitory earnings proxies, industry characteristics, and risk and growth proxies. While analysts forecasts capture 45–83% of the information from these sources depending on model specifications, they do not appear to fully incorporate certain information items. In particular, proxies for conservative accounting and transitory earnings are incrementally useful in predicting future earnings; proxies for economic rents, conservative accounting, and risk are incrementally useful in explaining the market-to-book ratio. Collectively, these results validate the use of analysts forecasts as a parsimonious proxy for forward-looking information in accounting-based valuation and suggest how to improve on their use.JEL Classification: D4, G12, M4     

Additional utility of insiders with imperfect dynamical information

In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insiders information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.Received: 1 October 2003, Mathematics Subject Classification: 60G48, 90A09, 60H07, 90A60JEL Classification: D82, G11, G14     

Takeover motives in a weak regulatory environment surrounding a market shock: a case study of New Zealand with a comparison of Gondhalekar and Bhagwat’s (2003) US findings

We examine the motives for takeovers in New Zealand surrounding the 1987 stock market crash and compare with the US findings of Gondhalekar and Bhagwat (2003). There are a number of structural differences between the New Zealand and US markets that could impact on merger motives. Compared with the US, New Zealand is a small capital market; with weak takeover regulation and a prolonged aftermath of the 1987 stock market crash. Consistent with US research, we find evidence of synergy and hubris motivations in New Zealand takeovers although we find the synergy motivation is stronger. Contrary to expectations we find no evidence of agency motivated takeovers.

Edokko Options: A New Framework of Barrier Options

In this paper, we will give a new framework of barrier options to generalize`Parisian Option' and `Delayed Barrier Option'. Take a stopping time asthe caution time. When occurs, derivatives are given `Caution'. After, if K.O. time =() occurs, derivative contractsvanish. We simply say that first `Caution' second `K.O.'. Using thisframework, designs of barrier options become more flexible than before and newrisk management will be possible. New barrier options in this category arecalled Edokko Options or Tokyo Options.     

Estimating the term structures of corporate debt

This paper investigates the corporate bond market by estimating monthly interest rate term structures for investment grade credit classes using both S&P's and Moody's ratings. Term structures are modeled by a piecewise constant forward rate curve and estimated on noncallable coupon paying bonds issued by industrial firms. The iterative estimation algorithm minimizes the sum of squared errors between market prices and model prices while identifying and removing outliers from the sample. Although the forward rate model is successful at pricing corporate debt, additional factors are found to be significant at explaining the residual price error that remains after the forward rate model is fit to market prices. Six necessary no-arbitrage conditions are derived for the term structures of risky and risk-free debt. Occasionally, some of these no-arbitrage conditions are violated and a few violations are asymptotically statistically significant. Finally, trading strategies that capture mispricing in the corporate debt market and violations of no-arbitrage bounds are discussed.This paper was adapted from my dissertation, completed at Cornell University. An earlier version of this paper was titled The Term Structures of Corporate Debt. Thanks to participants at the Cornell University finance workshop, Warren Bailey, Peter Carr, Antoine Giannetti, and especially Robert Jarrow for their helpful comments.     

Multi-agent investment in incomplete markets

The problem of the expected utility maximization in incomplete markets for a single agent is well understood in a fairly general setting. This paper studies the problem for the multi-agent case. For this case a cooperative investment game is posed as follows: firstly collect all agents capital together at the initial time, then invest the total capital in a trading strategy, and finally divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of Pareto optimal cooperative strategies and a characterization of situations where cooperation strictly Pareto dominates non cooperation, and prove that the core of the cooperative investment game is non-empty under mild conditions using Scarf theorem.Received: August 2003, Mathematics Subject Classification (1991): 91B28, 91A12, 60H30JEL Classification: G11, C71This work is supported by the National Natural Science Foundation of China under grant 10201031. It is a pleasure for the author to express his sincere thanks to an anonymous referee for valuable suggestions.     

Investor protection, adverse selection, and the probability of informed trading

The purpose of this study is to investigate the relation between investor protection, adverse selection, and the probability of informed trading. Previous research has established a direct relation between investor protection and firm liquidity, measured by bid-ask spreads and depths. In this study, we test the hypothesis that adverse selection is the mechanism through which poor investor protection leads to higher costs of liquidity. The Hong Kong equity market provides a unique opportunity to compare adverse selection differences across distinct investor protection environments, holding constant the trading platform and currency. Using various bid-ask spread decomposition models and probability of informed trading estimates, we confirm the hypothesized relation between investor protection quality and adverse selection costs. These findings contribute to the literature by establishing one of the links in the chain connecting investor protection to firm valuation.