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Incomplete Markets (incomplete + market)
Selected AbstractsPRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTUREMATHEMATICAL FINANCE, Issue 3 2004Virginia R. Young We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete. [source] A Comparison of Two Quadratic Approaches to Hedging in Incomplete MarketsMATHEMATICAL FINANCE, Issue 4 2001David Heath This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-variance hedging in a class of stochastic volatility models. We explain the theory for both hedging approaches in a general framework, specialize to a Markovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical results are obtained mainly by PDE and simulation methods. In addition, we take special care to check that all of our examples do satisfy the conditions required by the general theory. [source] The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete MarketsMATHEMATICAL FINANCE, Issue 1 2000Marco Frittelli Let , be a family of stochastic processes on a given filtered probability space (,, F, (Ft)t,T, P) with T,R+. Under the assumption that the set Me of equivalent martingale measures for , is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to P, in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy. [source] HEDGING BY SEQUENTIAL REGRESSIONS REVISITEDMATHEMATICAL FINANCE, Issue 4 2009Almost 20 years ago Föllmer and Schweizer (1989) suggested a simple and influential scheme for the computation of hedging strategies in an incomplete market. Their approach of,local,risk minimization results in a sequence of one-period least squares regressions running recursively backward in time. In the meantime, there have been significant developments in the,global,risk minimization theory for semimartingale price processes. In this paper we revisit hedging by sequential regression in the context of global risk minimization, in the light of recent results obtained by ,erný and Kallsen (2007). A number of illustrative numerical examples are given. [source] PRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTUREMATHEMATICAL FINANCE, Issue 3 2004Virginia R. Young We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete. [source] Default and Punishment in General Equilibrium,ECONOMETRICA, Issue 1 2005Pradeep Dubey We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment by thinking of assets as pools. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of adverse selection and signalling phenomena in a perfectly competitive, general equilibrium framework. Perfect competition eliminates the need for lenders to compute how the size of their loan or the price they quote might affect default rates. It also makes for a simple equilibrium refinement, which we propose in order to rule out irrational pessimism about deliveries of untraded assets. We show that refined equilibrium always exists in our model, and that default, in conjunction with refinement, opens the door to a theory of endogenous assets. The market chooses the promises, default penalties, and quantity constraints of actively traded assets. [source] Risk-free bond prices in incomplete markets with recursive multiple-prior utilitiesINTERNATIONAL JOURNAL OF ECONOMIC THEORY, Issue 2 2006Chiaki Hara D52; D91; E21; E44; G12 We consider an exchange economy under uncertainty, in which agents' utility functions may be recursive and the expected utility calculation may be based on multiple priors. The utility functions representing risk attitudes and intertemporal substitution are negative exponential functions. These utility functions and the access to asset markets may arbitrarily differ across agents. We prove that the risk-free bond price goes down (and the interest rate goes up) monotonically as the market incompleteness diminishes. We also find the range of equilibrium bond prices that depends on the primitives of the economy but not on the structures of asset markets. [source] Monetary Policy under Alternative Asset Market Structures: The Case of a Small Open EconomyJOURNAL OF MONEY, CREDIT AND BANKING, Issue 7 2009BIANCA DE PAOLI welfare; optimal monetary policy; asset markets; small open economy Can the structure of asset markets change the way monetary policy should be conducted? Following a linear-quadratic approach, the present paper addresses this question in a New Keynesian small open economy framework. Our results reveal that the configuration of asset markets significantly affects optimal monetary policy and the performance of standard policy rules. In particular, when comparing complete and incomplete markets, the ranking of policy rules is entirely reversed, and so are the policy prescriptions regarding the optimal level of exchange rate volatility. [source] Household Debt and Income Inequality, 1963,2003JOURNAL OF MONEY, CREDIT AND BANKING, Issue 5 2008MATTEO IACOVIELLO income inequality; household debt; credit constraints; incomplete markets I construct an economy with heterogeneous agents that mimics the time-series behavior of the earnings distribution in the United States from 1963 to 2003. Agents face aggregate and idiosyncratic shocks and accumulate real and financial assets. I estimate the shocks that drive the model using data on income inequality, aggregate income, and measures of financial liberalization. I show how the model economy can replicate two empirical facts: the trend and cyclical behavior of household debt and the diverging patterns in consumption and wealth inequality over time. While business cycle fluctuations can account for the short-run changes in household debt, its prolonged rise of the 1980s and the 1990s can be quantitatively explained only by the concurrent increase in income inequality. [source] RISK INDIFFERENCE PRICING IN JUMP DIFFUSION MARKETSMATHEMATICAL FINANCE, Issue 4 2009Bernt Øksendal We study the risk indifference pricing principle in incomplete markets: The (seller's),risk indifference price,,is the initial payment that makes the,risk,involved for the seller of a contract equal to the risk involved if the contract is not sold, with no initial payment. We use stochastic control theory and PDE methods to find a formula for,,and similarly for,. In particular, we prove that ,where,plow,and,pup,are the lower and upper hedging prices, respectively. [source] COHERENT ACCEPTABILITY MEASURES IN MULTIPERIOD MODELSMATHEMATICAL FINANCE, Issue 4 2005Berend Roorda The framework of coherent risk measures has been introduced by Artzner et al. (1999; Math. Finance 9, 203,228) in a single-period setting. Here, we investigate a similar framework in a multiperiod context. We add an axiom of dynamic consistency to the standard coherence axioms, and obtain a representation theorem in terms of collections of multiperiod probability measures that satisfy a certain product property. This theorem is similar to results obtained by Epstein and Schneider (2003; J. Econ. Theor. 113, 1,31) and Wang (2003; J. Econ. Theor. 108, 286,321) in a different axiomatic framework. We then apply our representation result to the pricing of derivatives in incomplete markets, extending results by Carr, Geman, and Madan (2001; J. Financial Econ. 32, 131,167) to the multiperiod case. We present recursive formulas for the computation of price bounds and corresponding optimal hedges. When no shortselling constraints are present, we obtain a recursive formula for price bounds in terms of martingale measures. [source] Household Heterogeneity and Real Exchange Rates,THE ECONOMIC JOURNAL, Issue 519 2007Narayana R. Kocherlakota We assume that individuals can fully insure themselves against cross-country shocks but not against individual-specific shocks. We consider two particular models of limited risk-sharing: domestically incomplete markets (DI) and private information,Pareto optimal (PIPO) risk-sharing. For each model, we derive a restriction relating the cross-sectional distributions of consumption and real exchange rates. We evaluate these restrictions using household-level consumption data from the US and the UK. We show that the PIPO restriction fits the data well when households have a coefficient of relative risk aversion of around 5. The restrictions implied by the complete risk-sharing model and the DI model fare poorly. [source] Heterogeneity, Efficiency and Asset Allocation with Endogenous Labor Supply: The Static CaseTHE MANCHESTER SCHOOL, Issue 3 2001Marcelo Bianconi We study the implications of consumption and labor allocations with ex ante efficiency and possibly ex post inefficiency on international/interregional portfolio diversification. The answers we obtain depend crucially on the market regime relative to unemployment insurance. If there are complete markets for unemployment insurance, changes in asset allocation are small in the presence of ex post inefficiency, but if there are incomplete markets for unemployment insurance, changes in asset allocation can be large. The direction of the asset movement is towards more diversification. [source] | |||||||||||||||||||