In financial analysis risk
quantification is essential for efficient portfolio management in a stochastic
framework. In this paper we study the value at risk, the expected shortfall, marginal
expected shortfall and value at risk, incremental value at risk and expected
shortfall, the marginal and discrete marginal contributions of a portfolio.
Each asset in the portfolio is characterized by a trend, a volatility and a
price following a three-dimensional diffusion process. The interest rate of
each asset evolves according to the Hull and White model. Furthermore, we
propose the optimization of this portfolio according to the value at risk
model.
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