Cox, J. and Huang, C-F. (1989). Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process, Journal of Economic Theory, 49, 33-83.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of several technical flaws and gaps, this paper attracted a lot of attention and made a strong impact on the future development of the field of consumption investment models. In fact, this paper perpetuated numerous corrections and amelioration of Merton s original version (e.g. 41] 40] [14], 56] 57] 21] to name a few) which in turn stimulated development of an entirely new area within the classical finance, based primarily on the tools and techniques of the control theory. A comprehensive list of literature on diffusion consumption investment models can be found in [46] and ....

Cox, J. and Huang, C-F. (1989). Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process, Journal of Economic Theory, 49, 33-83.

....corporation. The second non linear term determines the intertemporal behavior of the corporation and, therefore, the way the exchange rate risk is hedged. In the next section the equation (2.8) will be solved. We will implement a transformation method first introduced in finance by Cox and Huang [6]. We will then obtain a second order linear partial di#erential equation of parabolic type the solution of which will allow us to derive the optimal hedge. 3 Exact solution of the model In this section we will transform the di#erential equation (2.8) to render it linear. This can be accomplished ....

J. C. Cox and C. fu Huang, Optimal consumption and portfolio policies when asset prices follow a di#usion process, Journal of Economic Theory, 49 (1989), pp. 33--83.

....utility functions, then one can solve for the optimal consumption and investment rules in closed form. Merton s analysis relied on Markov state processes and sought to obtain explicit solutions to the Hamilton Jacobi Bellman equation in this context. Subsequently, Pliska [26] Cox and Huang [5], and Karatzas, Lehoczky and Shreve [16] all showed how to solve these problems in a non Markovian context by applying stochastic duality theory in the context of complete markets. Our interest here is in determining optimal strategies for investing in derivative assets such as options of various ....

....may now be formalized as: Program A max [w( U = E P u[W (#) subject to : e rt W (t) W 0 t # 0 # # # W (s ) # e w(x,s) 1 # [m(#; dx, ds) kQ (x)dxds] and W (t) # 0 almost surely. Due to the completeness of the financial market, it is well known (Cox and Huang [5], Karatzas and Shreve [17] that the investor s dynamic investment problem can be converted into the following static variational problem: Program A # Max # E P [u(#) subject to : E Q # e r# # # = W (0) In exactly the same manner as that of chapter 3 of Karatzas and Shreve [17] we ....

Cox, J.C. and Huang, C.F., 1989, "Optimal Consumption and Portfolio Policies when Asset Prices follow a Di#usion Process," Journal of Economic Theory, 49, 33-83.

....of Markovian asset prices, is based on duality characterizations of portfolios provided by the set of martingale measures. For the case of a complete financial market, where the set of martingale measures is a singleton, this martingale methodology was developed by Pliska [P 86] Cox and Huang [CH 89] CH 91] and Karatzas, Lehoczky and Shreve [KLS 87] It was shown that the marginal utility of the terminal wealth of the optimal portfolio is proportional to the density of the martingale measure; this key result naturally extends the classical Arrow Debreu theory of an optimal investment ....

J.C. Cox, C.F. Huang, (1989), Optimal consumption and portfolio policies when asset prices follow a diffusion process. J. Economic Theory, Vol. 49, pp. 33--83.

....under uncertainty, it has two important limitations: first, dynamic programming can only be used to find an optimal solution if the derived utility function is continuously di#erentiable. Second, the nonlinear nature of the Hamilton Jacobi Bellman equation renders it di#cult to solve. Recently, Cox and Huang (1989) and Karatzas, Lehoczky, and Shreve (1987) have developed an alternative method for solving optimal consumption portfolio problems using a martingale representation technology. Their martingale methods have two advantages over stochastic dynamic programming: first, they do not require ....

....context of optimal asset al..location and retirement incentives but without regard for work leisure flexibility. Modelling The Retirement Decision 3 The model developed in this paper is a martingale characterisation of the intertemporal model of consumption and portfolio choice which is due to Cox and Huang (1989) and Karatzas, Lehoczky, and Shreve (1987) Furthermore, it uses the application of duality theory developed by Xu and Shreve (1992) and He and Pages (1993) in solving the intertemporal optimization problem is characterized by the martingale representation technology. The inclusion of labour ....

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Cox, J. C., and C.-F. Huang (1989): "Optimal Consumption and Portfolio Policies When Asset Prices Follow a Di#usion Process," Journal of Economic Theory, 49, 33--83.

....(1979) and Harrison Pliska (1981) introduced the martingale methodology to finance. They relate absence of arbitrage and completeness of securities markets to the existence resp. uniqueness of equivalent martingale measures. Their results were applied by Pliska (1986) Karatzas et al. 1987) and Cox Huang (1989) to portfolio optimization in complete models. With the help of the pricing measure, they can determine the optimal terminal wealth basically as in a simple one period model. The corresponding generating trading strategy is computed in a second step. Using a different terminology, this alternative ....

Cox, J. and C.-F. Huang (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory 49, 33--83.

....and Harrison Pliska (1981) introduced the martingale methodology to finance. They relate absence of arbitrage and completeness of securities markets to the existence resp. uniqueness of equivalent martingale measures. Their results were applied by Pliska (1986) Karatzas et al. 1987) and Cox Huang (1989) to portfolio optimization in complete models. With the help of the pricing measure, they can determine the optimal terminal wealth basically as in a simple one period model. The corresponding Institut fr Mathematische Stochastik, Universitt Freiburg, Eckerstrae 1, D 79104 Freiburg i. Br. ....

Cox, J. and C.-F. Huang (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory 49, 33--83.

....#1990#, and Dumas and Luciano #1991# with a somewhat di#erent optimality criteria, and by Leland #1985#, Merton #1989#, Shen #1990#, and Boyle and Vorst #1991# without an explicit optimality criteria. 3: Leverage and nonnegative wealth constraints are analyzed by Grossman and Vila #1992# and Cox and Huang #1989#, respectively, with a somewhat di#erent optimality criterion. 4: In continuous time mathematical #nance literature, an abstract stochastic control representation for the minimum cost hedging problem is derived and some bounds and complicate approximation schemes for computing them are provided. ....

COX J.C. and HUANG C. #1989#, #Optimal Consumption and Portfolio Policies When Asset Prices Follow A Di#usion Process", Journal of Economic Theory, 49, 33-83.

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Cox, J. and Huang, C-F. (1989). Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process, Journal of Economic Theory, 49, 33-83.

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Cox J.C. and C-F Huang, "Optimal consumption and portfolio policies when asset prices follow a di#usion process", Journal of Economic Theory 49(1989)33-83

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J.C. Cox, C.F. Huang, (1989), Optimal consumption and portfolio policies when asset prices follow a di#usion process. J. Economic Theory, Vol. 49, pp. 33--83.

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Cox, J.C. and C.-f. Huang (1989) \Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diusion Process", Journal of Economic Theory 49, 33-83.

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Cox, J.C., and Huang, C-F. (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49, 33-83.

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Cox, J.C. and C. Huang, 1991, "Optimal Consumption and Portfolio Policies When Asset Prices Follow Diffusion Process", Journal of Economic Theory, 49, 33-83.

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Cox, J., and C.F. Huang, 1989, \Optimal Consumption and Portfolio Policies When Asset Prices Follow a Diusion Process. " Journal of Economic Theory 36, 33-83.

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Cox, J., and C.F. Huang, 1989, \Optimal Consumption and Portfolio Policies When Asset Prices Follow a Diusion Process," Journal of Economic Theory 49, 33-83.

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J.C. Cox and C.F. Huang, "Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process," J. Econ. Theory, 49, (1989), 33-83.

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Cox, J. and Huang, C.F. (1989) Optimal consumption and portfolio policies when asset prices folllow a diffusion process. J. Econ. Theory 49, 33-83.

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