A continuous-time portfolio turnpike theorem

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Abstract

We prove a continuous-time portfolio turnpike theorem. The proof uses the theory of martin-gales and is more intuitively appealing than the usual discrete-time mode of proof using dynamic programming. When the interest rate is strictly positive, the present value of any contingent claim having payoffs bounded from above can be made arbitrarily small when the investment horizon increases. Thus an investor concentrates his wealth in buying contingent claims that have payoffs unbounded from above at the very beginning of his horizon. As a consequence, it is the asymptotic property of his utility function as wealth goes to infinity that determines his optimal investment strategy at the very beginning of his horizon.

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Cited by (19)

  • Turnpike property and convergence rate for an investment model with general utility functions

    2015, Journal of Economic Dynamics and Control
    Citation Excerpt :

    As a consequence, it is the asymptotic property of his utility function as wealth goes to infinity that determines his optimal investment strategy at the very beginning of his horizon.”, see Cox and Huang (1992). It is natural and interesting to ask if the turnpike property (1.2) still holds for general utilities (strictly increasing, continuous and concave, but not necessarily continuously differentiable and strictly concave) and if the error estimate (1.3) can be established and the convergence rate and the error magnitude can be computed.

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This is a revised version of the second half of our earlier paper titled ‘A Variational Problem Arising in Financial Economics with an Application to a Portfolio Turnpike Theorem’. We would like to thank Robert Merton and Stephen Ross for helpful conversations.

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