Abstract
We consider the non-adapted version of a simple problem of portfolio optimization in a financial market that results from the presence of insider information. We analyze it via anticipating stochastic calculus and compare the results obtained by means of the Russo-Vallois forward, the Ayed-Kuo, and the Hitsuda-Skorokhod integrals. We compute the optimal portfolio for each of these cases with the aim of establishing a comparison between these integrals in order to clarify their potential use in this type of problem. Our results give a partial indication that, while the forward integral yields a portfolio that is financially meaningful, the Ayed-Kuo and the Hitsuda-Skorokhod integrals do not provide an appropriate investment strategy for this problem.
Highlights
Many mathematical models in the applied sciences are expressed in terms of stochastic differential equations such as: Under Insider Information
The aim of this work is to clarify the suitability of the use of each of these stochastic integrals in this particular portfolio optimization
The simplest situation is the one corresponding to the Russo-Vallois forward integral, that is, to the problem analyzed in Section 3; since f is a function of B( T ) such that f ∈ L∞ (R) and 0 ≤ f ≤ 1
Summary
This equation cannot be understood in the sense of the classical differential calculus of Leibniz and Newton. The choice of a particular notion of stochastic integration has generated a debate that has expanded along decades [1,2]
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