| Abstract : | The paper is organized as follows. Chapter 2 a basic notion of some financial concept like option, random walk, Brownian Motion, stock price process, Black-Scholes option pricing model and finally Value at Risk. In chapter 3, we calculate the VaR of the unhedged position. In chapter 4, we compute the VaR of a partially hedged position. Chapter 5 presents the distribution of the future value V t+τ of the hedged asset. Chapter 6 provides and solves the institution’s main optimization problem, which briefly said, is the minimization of the VaR under some constraints.Chapter 7 constructs and illustrates the comparative statics results. In chapter 8 we provide an example of optimal hedging. Chapter 9 concludes our analysis.
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