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**1 - 1**of**1**### Approximate Series and Claim Replicating Problems for a Market With Time Varying Random Volatility

"... The paper investigates a contingent claim replicating problem for a diffusion market model. It is proposed an approach which does not call to solve the backward parabolic equation, unlike for the classical method, and this approach is applied for a case when the volatility coefficient is random and ..."

Abstract
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The paper investigates a contingent claim replicating problem for a diffusion market model. It is proposed an approach which does not call to solve the backward parabolic equation, unlike for the classical method, and this approach is applied for a case when the volatility coefficient is random and depends on time. The replicating strategy is decomposed to series of explicit strategies which does not use current estimations of volatility. A mean variance convergence of the series is proved. Keywords: diffusion market model, option pricing, time varying random volatility, approximate series 1 Introduction The paper investigates optimal investment problem and hedging problem for a market which consists of a risks free bond and a risky stock. It is assumed that the dynamics of the stock is described by a diffusion random process. The dynamics of the bond is deterministic and exponentially increasing with a given risk free rate. The most well-known strategies for this market model were ob...