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25
Applying the HJMapproach when volatility is stochastic. Working paper
, 1998
"... stochastic volatility. ’ Of course, the authors take the full blame for any remaining error. Please address all correspondence ..."
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stochastic volatility. ’ Of course, the authors take the full blame for any remaining error. Please address all correspondence
Consumption Commitments: A Foundation for ReferenceDependent Preferences and Habit Formation
, 2010
"... We build a theory of referencedependent preferences based on adjustment costs in consumption. The main contribution of the theory is that it endogenizes the evolution of the reference point. The reference point generated by our model exhibits several features exogenously assumed in existing theorie ..."
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We build a theory of referencedependent preferences based on adjustment costs in consumption. The main contribution of the theory is that it endogenizes the evolution of the reference point. The reference point generated by our model exhibits several features exogenously assumed in existing theories: it (1) re‡ects recent expectations, (2) depends on past consumption levels, and (3) diminishes in importance when agents experience large shocks. When the ratio of idiosyncratic to aggregate risk is large, the model is approximately equivalent to standard habit formation speci…cations in which the reference point is a weighted average of past consumption. We illustrate the implications of endogenizing the reference point using three applications: aggregate consumption dynamics, changes in policy parameters, and the welfare cost of shocks. In each application, our model of endogenous reference points con…rms certain intuitions from existing theories but yields some starkly di¤erent predictions. For example, reducing idiosyncratic risk can raise the welfare cost of aggregate shocks by making reference points more persistent.
Growth Optimal Investment and Pricing of Derivatives
, 1999
"... We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growthoptimal strategies should be particularly relevant to the problem of pricing derivatives. Under the assumption ..."
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We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growthoptimal strategies should be particularly relevant to the problem of pricing derivatives. Under the assumptions of no trading costs, and no restrictions on lending, we find an appropriate equivalent martingale measure that prices the underlying and the derivative security. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is check with a smallscale empirical test. 1 This work was supported by the NFR contract SFO 1778302 2 and by I.N.F.M. grantinaid Preprint submitted to Elsevier Preprint 1 February 2008 1
On an Optimal Consumption Problem for PIntegrable Consumption Plans
"... this paper to a stochastic timedependent situation, simply by a suitable choice of the underlying measure space. In addition to the space\Omega of states of nature, whose distribution is given by the (probability) measure ¯, there is now also a time interval [0; T ] and a filtration fF t : t 2 [0; ..."
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this paper to a stochastic timedependent situation, simply by a suitable choice of the underlying measure space. In addition to the space\Omega of states of nature, whose distribution is given by the (probability) measure ¯, there is now also a time interval [0; T ] and a filtration fF t : t 2 [0; T ]g of information oealgebras
An Alternative Approach for Valuing Continuous Cash Flows
, 2000
"... We consider the problem of replicating the payoffs from variable annuities with a continuous cash flow given by a function of some traded asset's price. The standard approaches involve either dynamic trading in this underlying asset or a static position in a continuum of options of all strikes and m ..."
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We consider the problem of replicating the payoffs from variable annuities with a continuous cash flow given by a function of some traded asset's price. The standard approaches involve either dynamic trading in this underlying asset or a static position in a continuum of options of all strikes and maturities. We present an alternative approach which combines dynamic trading in the underlying asset with a static position in options of a single maturity. In many instances, our approach yields explicit valuation formulas and hedging strategies when the volatility of the underlying is an arbitrary function of its price.
Pierre Collin Dufresne
"... In recentyears results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we showhow efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for sever ..."
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In recentyears results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we showhow efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for several new classes of exotic options including the cliquet, the ladder, the discrete shout and the discrete lookback. We also provide a derivation of the price of an option on the maximum of n assets to demonstrate the power of the multidimensional Girsanov theorem. Although some of the results presented are well known, the treatment of the material in this paper is new in that it focuses on the application of the martingale technology to concrete problems in option pricing, methods that until nowhave mostly been used for purely theoretical purposes.
Intertemporal MeanVariance Efficiency with a Markovian State Price Density ∗
, 2003
"... This paper extends Merton’s continuous time (instantaneous) meanvariance analysis and the mutual fund separation theory. Given the existence of a Markovian state price density process, the optimal portfolios from concave utility maximization are instantaneously meanvariance efficient independent o ..."
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This paper extends Merton’s continuous time (instantaneous) meanvariance analysis and the mutual fund separation theory. Given the existence of a Markovian state price density process, the optimal portfolios from concave utility maximization are instantaneously meanvariance efficient independent of the concave utility function’s form. The Capital Asset Pricing Model holds with the market portfolio induced by the growth optimal portfolio. The MarkowitzTobin mutual fund separation is extended to include the lognormal assumption for asset prices as a special case. Closed form solutions to the expected utility maximization of terminal portfolio value are derived. We present an example in which the state price processes are specified as a multivariate geometric Brownian motion and the asset prices follow a multivariate diffusion process with relatively general parameters.
Dynamic Downside Risk Measure and Optimal Investment Behaviors
, 2007
"... This article highlights the importance of investors’downsiderisk concerns, and examines optimal investment behaviors in a dynamic downsiderisk framework. The authors does not only derive an analytical expression of investors ’ optimal behaviors, but also provide economic insights of the properties ..."
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This article highlights the importance of investors’downsiderisk concerns, and examines optimal investment behaviors in a dynamic downsiderisk framework. The authors does not only derive an analytical expression of investors ’ optimal behaviors, but also provide economic insights of the properties of the downside risk measure and optimal investment strategies using comparative statics. It sheds light on both academic and practical applications of dynamic belowtarget semivariance model to the …elds of risk management and investment decision making.
Personal File Reference: hybrid7.tex
, 2000
"... We consider the problem of replicating the payoffs from variable annuities with a continuous cash flow given by a function of some traded asset’s price. The standard approaches involve either dynamic trading in this underlying asset or a static position in a continuum of options of all strikes and m ..."
Abstract
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We consider the problem of replicating the payoffs from variable annuities with a continuous cash flow given by a function of some traded asset’s price. The standard approaches involve either dynamic trading in this underlying asset or a static position in a continuum of options of all strikes and maturities. We present an alternative approach which combines dynamic trading in the underlying asset with a static position in options of a single maturity. In many instances, our approach yields explicit valuation formulas and hedging strategies when the volatility of the underlying is an arbitrary function of its price.
Investment Optimization under Constraints
, 2003
"... We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some “imperfection”, such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under co ..."
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We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some “imperfection”, such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002) [PhM], Long (2002) [L02a]. We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999) [KSch].