FBSDE approach to utility portfolio selection in a market with random parameters

Ferland, René; Watier, François

doi:10.1016/j.spl.2007.07.016

Cited by 9 publications

(6 citation statements)

References 14 publications

(15 reference statements)

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“…Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization of the optimal portfolio for general utility functions in terms of a forward-backward stochastic differential equation (FBSDE) and derive solutions for a number of well-known utility functions. Our results complement a previous study conducted in Ferland and Watier (2008) on optimal strategies in markets driven by Brownian noise with random drift and volatility parameters.…”

supporting

confidence: 87%

“…which is identical to the BSDE derived for the power utility case in Ferland and Watier (2008) when the noise process is a Brownian motion; with Y π * t playing the role of p t and σ π * t replacing Σ −1/2 t Λt pt . Therefore, we can lean on the results obtained in that paper, in particular, the form of the optimal solution when the model parameters are deterministic.…”

Section: Optimalitymentioning

confidence: 62%

“…Cvitanić and Karatzas (1992) uses similar techniques to solve a constrained version of the portfolio optimization problem. More recently, Ferland and Watier (2008) utilizes the stochastic Pontryagin maximum principle to characterize the optimal portfolio in terms of a forward-backward stochastic differential equation (FBSDE) for a market with random parameters driven by Brownian noise and a general utility function. Rieder and Wopperer (2012) apply the same technique to solving a robust version of the same problem where utility maximization is performed under the worst-case parameter configuration.…”

Section: Introductionmentioning

confidence: 99%

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A Variational Analysis Approach to Solving the Merton Problem

Al-Aradi,

Jaimungal

2020

Preprint

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We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization of the optimal portfolio for general utility functions in terms of a forward-backward stochastic differential equation (FBSDE) and derive solutions for a number of well-known utility functions. Our results complement a previous study conducted in Ferland and Watier (2008) on optimal strategies in markets driven by Brownian noise with random drift and volatility parameters.

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supporting

confidence: 87%

Section: Optimalitymentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

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A Variational Analysis Approach to Solving the Merton Problem

Al-Aradi,

Jaimungal

2020

Preprint

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“…In the early 1990s Pardoux and Peng [10] introduced the notion of backward stochastic differential equations (BSDE) which provided the ideal tool for Lim and Zhou [11] to adequately solve the continuous-time mean-variance allocation problem in a Black-Scholes model with stochastic uniformly bounded market coefficients. It is worth mentioning that BSDE theory was also proved to be valuable in utility portfolio selection problems as shown in [12].Unfortunately, in these papers, the uniform boundedness hypothesis assumed for the interest rate process precludes the use of interest models such as Vasicek, Hull-White and Cox-Ingersoll-Ross (CIR) models which are highly valued by practitioners. In order to pass this limit a number of researchers drew on a more general market where in addition to the usual bank account and stocks an individual is allowed to invest part of his wealth in bonds or interest derivatives.…”

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confidence: 99%

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confidence: 99%

Mean–variance efficiency with extended CIR interest rates

Ferland¹,

Watier²

2009

Appl Stoch Models Bus & Ind

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We study a mean-variance investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. We construct a mean-variance efficient portfolio through the solutions of backward stochastic differential equations. We also give sufficient conditions under which an explicit analytic expression is available for the mean-variance optimal wealth of the investor. problem using the Hamilton-Jacobi-Bellman equation of dynamic programming. About 15 years later, the equivalent martingale measure concept developed by Harrison and Pliska [7] paved the way for solving several utility maximization problems in a market model with stochastic uniformly bounded parameters (see, for example, Karatzas [8]). Unfortunately one cannot adequately address the continuous-time mean-variance problem using one of the above techniques. This may explains in part why significant results were obtained only recently. Alternate methods had to be considered. For example, Duffie and Richardson [9] solved a deterministic market model mean-variance problem via orthogonal projection techniques. In the early 1990s Pardoux and Peng [10] introduced the notion of backward stochastic differential equations (BSDE) which provided the ideal tool for Lim and Zhou [11] to adequately solve the continuous-time mean-variance allocation problem in a Black-Scholes model with stochastic uniformly bounded market coefficients. It is worth mentioning that BSDE theory was also proved to be valuable in utility portfolio selection problems as shown in [12].Unfortunately, in these papers, the uniform boundedness hypothesis assumed for the interest rate process precludes the use of interest models such as Vasicek, Hull-White and Cox-Ingersoll-Ross (CIR) models which are highly valued by practitioners. In order to pass this limit a number of researchers drew on a more general market where in addition to the usual bank account and stocks an individual is allowed to invest part of his wealth in bonds or interest derivatives. Bajeux-Besnainou and Portait [13] incorporated a Vasicek interest rate model and zero-coupons bonds in their model and solved a mean-variance-type problem. But the Vasicek as well as the Hull-White model have a major drawback which is that there is a positive probability that one encounters negative values. Obviously, this is a highly unrealistic and undesirable feature in a real-world financial market. A few years later, Deelstra et al. [14] modified Bajeux-Besnainou and Portait's model by rather opting for a CIR interest rate process which is known to be almost surely positive under mild conditions. Applying essentially the martingale approach they obtained an optimal strategy for a power-utility maximization problem. Now the classical CIR process rely on three constant parameters, thus, from a practical point of view statistical fitting to real financial data may be greatly improved by considering a more flexible time-varying parameter model as shown in Maghsoodi's [15] study of 25 years of U.S. Treasury bill data....

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