Wealth-path dependent utility maximization in incomplete markets

Motivated by an optimal investment problem under time horizon uncertainty and when default may occur, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth-path dependent utility maximization problem. Our main result is an extension of the well-known dual formulation to this context. In contrast with the usual duality approach, we work directly on the primal problem. Sufficient conditions for characterizing the optimal solution are also provided in the case of complete markets, and are illustrated by examples.Received: December 2003, Mathematics Subject Classification (2000): 91B28, 91B16, 49N15, 49N30JEL Classification: G11The authors would like to thank the anonymous referees for their remarks and suggestions which greatly improved this paper. We also thank participants at the Oberwolfach workshop in 2003 for comments and discussions.     

A valuation algorithm for indifference prices in incomplete markets

A probabilistic iterative algorithm is constructed for indifference prices of claims in a multiperiod incomplete model. At each time step, a nonlinear pricing functional is applied that isolates and prices separately the two types of risk. It is represented solely in terms of risk aversion and the pricing measure, a martingale measure that preserves the conditional distribution of unhedged risks, given the hedgeable ones, from their historical counterparts.Received: 1 September 2003, Mathematics Subject Classification: 93E20, 60G40, 60J75JEL Classification: C61, G11, G13The second author acknowledges partial support from NSF Grants DMS 0102909 and DMS 0091946.     

Profitability of return and sentiment-based investment strategies in US futures markets

Our study adds to the literature by providing initial evidence on the interaction between short-horizon return predictability and investors’ sentiment by traders’ types on US commodity futures market. We find that the short-term contrarian profit is more associated with an increase rather than a decrease in hedgers’ sentiment. However, the interaction between lagged return and past change in speculators’ sentiment illustrates that the short-term contrarian profit is more associated with a decrease rather than an increase in sentiment. Based on behavioral finance theories, we conclude that hedgers behave like irrational traders while speculators behave like rational ones. Using Chou et al. (2007) decomposition, our results confirm the obtained relations between change in trader's sentiment and the overreaction. By expanding this decomposition, we find that the winners’ portfolio tends to more overreact with futures specific information. Also, the cross-autocorrelation between winners and losers and between losers and winners can represent another source of contrarian profits.     

Aggregate implications of indivisible labor, incomplete markets, and labor market frictions

We study the impact of tax and transfer programs on steady-state allocations in a model with search frictions, an operative labor supply margin, and incomplete markets. In a benchmark model that has indivisible labor and incomplete markets but no trading frictions we show that the aggregate effects of taxes are identical to those in the economy with employment lotteries, though individual employment and asset dynamics can be different. The effect of frictions on the response of aggregate hours to a permanent tax change is highly nonlinear. There is considerable scope for substitution between “voluntary” and “frictional” nonemployment in some situations.     

The interrelatedness of global equity markets, money markets, and foreign exchange markets

This article investigates different aspects of global financial markets, specifically relationships among equity markets, money markets, and foreign exchange markets across countries. To represent the three major financial markets of the world, Japan is the proxy for Asia, Germany is the proxy for Europe, and the United States is the proxy for North America. Strong evidence exists that international money markets and international equity markets are becoming increasingly integrated over time. This article incorporates foreign exchange values as partial determinants of equity returns and money market returns and investigates the interactions among these three asset markets from a global perspective.     

Risk measure pricing and hedging in incomplete markets

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so that the risk exposure will not increase. The associated optimal hedging portfolio is decided by minimizing a convex measure of risk. I will give the definition of risk-efficient options and confirm that options evaluated by risk measure pricing rules are indeed risk-efficient. Relationships to utility indifference pricing and pricing by valuation and stress measures will be discussed. Examples using the shortfall risk measure and average VaR will be shown. The work of Mingxin Xu is supported by the National Science Foundation under grant SES-0518869. I would like to thank Steven Shreve for insightful comments, especially his suggestions to extend the pricing idea from using shortfall risk measure to coherent ones, and to study its relationship to utility based derivative pricing. The comments from the associate editor and the anonymous referee have reshaped the paper into its current version. The paper has benefited from discussions with Freddy Delbaen, Jan Večeř, David Heath, Dmitry Kramkov, Peter Carr, and Joel Avrin.     

Consumption in incomplete markets

We develop a method to find approximate solutions, and their accuracy, to consumption–investment problems with isoelastic preferences and infinite horizon, in incomplete markets where state variables follow a multivariate diffusion. We construct upper and lower contractions; these are fictitious complete markets in which state variables are fully hedgeable, but their dynamics is distorted. Such contractions yield pointwise upper and lower bounds for both the value function and the optimal consumption of the original incomplete market, and their optimal policies are explicit in typical models. Approximate consumption–investment policies coincide with the optimal one if the market is complete or utility is logarithmic.     

Pricing options in incomplete equity markets via the instantaneous Sharpe ratio

We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Saá-Requejo (J Polit Econ 108:79–119, 2000) and of Björk and Slinko (Rev Finance 10:221–260, 2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque et al. (Derivatives in financial markets with stochastic volatility. Cambridge University Press, 2000).     

Pricing derivatives of American and game type in incomplete markets

In this paper the neutral valuation approach is applied to American and game options in incomplete markets. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. Game contingent claims are derivative contracts that can be terminated by both counterparties at any time before expiration. They generalize American options where this right is limited to the buyer of the claim. It turns out that as in the complete case, the price process of American and game contingent claims corresponds to a Snell envelope or to the value of a Dynkin game, respectively.On the technical level, an important role is played by -sub- and -supermartingales. We characterize these processes in terms of semimartingale characteristics.Received: June 2003, Mathematics Subject Classification (2000):   91B24, 60G48, 91B16, 91A15, 60G40JEL Classification:   G13, D52, C73The authors want to thank PD Dr. Martin Beibel for the idea leading to the proof of Proposition A.4 and both anonymous referees for many valuable comments. The second author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through the Graduiertenkolleg Angewandte Algorithmische Mathematik at Munich University of Technology and by the Fonds zur Förderung der wissenschaftlichen Forschung at Vienna University of Technology.     

An investigation of the benefits of portfolio investment in Central and Eastern European stock markets

This paper: (i) examines the potential benefits from diversifying into eight stock markets of Central and Eastern Europe (CEE); and (ii) quantifies the importance of country, industry and time factors in CEE equity returns. The findings suggest that substantial benefits exist from investing in CEE stock markets and that they accrue more from the geographical spread than from the industrial mix of the equities included in the portfolio. However, the returns earned by CEE equities vary dramatically over time. This variability may hamper the efforts of investors attempting to exploit the diversification “free lunch”.     

Predictability of stock markets with disequilibrium trading

This paper analyses the predictability of a hypothetical market with freely negotiated prices on which exists a censoring of one-period returns which are in excess of an arbitrary level (‘floor’ and ‘ceiling’). It is shown that the expected value of returns (adjusted for drift) conditional on last period information regarding the censoring are equal to zero (and therefore the market is not predictable in mean) if there is no intertemporal spillover on the market. A simple simulation model is proposed and applied for the analysis of the effects of intertemporal and cross-spillovers resulting from quantity constraints. Statistical predictability tests are proposed, based on the corrected Student-t statistic of a regression of returns of some information concerning the previous censoring. An illustrative empirical analysis of six main time series of returns on the Warsaw Stock Exchange confirms their ex-ante, but not ex-post, predictability.     

Information linkages between emission allowance and energy markets

We employ a rational expectations framework similar to that proposed by Fleming et al. (1998) to examine the source, and nature of, information linkages between the emission allowance and energy markets as gauged by the correlation of return volatilities. Estimating the model for bivariate pairings of securities suggests that market linkages arise from sensitivities to common information rather than from indirect spillovers, with emission allowances most strongly linked to the crude oil market.     

Weighted norm inequalities and hedging in incomplete markets

Let be an -valued special semimartingale on a probability space with canonical decomposition . Denote by the space of all random variables , where is a predictable -integrable process such that the stochastic integral is in the space of semimartingales. We investigate under which conditions on the semimartingale the space is closed in , a question which arises naturally in the applications to financial mathematics. Our main results give necessary and/or sufficient conditions for the closedness of in . Most of these conditions deal with BMO-martingales and reverse H?lder inequalities which are equivalent to weighted norm inequalities. By means of these last inequalities, we also extend previous results on the F?llmer-Schweizer decomposition.     

Asian equity markets: growth,opportunities, and challenges

Asian equity markets have grown significantly in size since the early 1990s, driven by strong international investor inflows, growing regional financial integration, capital account liberalization, and structural improvements to markets. The development of equity markets provides a more diversified set of channels for financial intermediation to support growth, thus bolstering medium-term financial stability. At the same time, as highlighted by the May–June 2006 market corrections, the increasing role of stock markets potentially changes the nature of macroeconomic and financial stability risks, as well as the policy requirements for dealing with these risks.     

Financial reforms and time-varying microstructures in emerging equity markets

This paper seeks to investigate the impact of financial reforms on time-varying microstructures in emerging equity markets. We develop annual indicators of informational efficiency, market volatility and transaction costs, using daily data for a panel of 28 emerging markets over the 1996–2007 period. We then analyze the impact of insider trading regulations, trading system automation and accounting standardization on microstructures through a set of panel regressions controlling for financial development and simultaneous reforms. Our results suggest that emerging market microstructures are affected by economic and political context, are strongly related to one another and depend on specific institutional reforms.