Our goal is to resolve a problem proposed by Karatzas and Fernholz  (2008) : Characterizing  the minimum amount of initial capital that would guarantee the investor to beat the market portfolio with a certain probability  as a function of the market configuration and time to maturity. We show that this value function is the smallest  supersolution of a non-linear PDE. As in Karatzas and Fernholz  (2008)  , we do not assume the existence of an equivalent local martingale measure  but merely the existence of a local martingale deflator.
Our goal is to resolve a problem proposed by Fernholz and Karatzas On optimal arbitrage (2008) Columbia Univ. : to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability , as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas On optimal arbitrage (2008) Columbia Univ. , we do not assume the existence of an equivalent local martingale measure , but merely the existence of a local martingale deflator.
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Karatzas and Fernholz
Fernholz and Karatzas
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On optimal arbitrage
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: Characterizing
Columbia Univ.
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: to characterize
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that would guarantee the investor to
with which an investor can
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,
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nonnegative viscosity
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non-linear
nonlinear
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Karatzas and Fernholz
Fernholz and Karatzas
A
On optimal arbitrage
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Columbia Univ.
A
,