Financial investment risk prediction

Financial investment risk prediction?

In the financial market, there are numerous of ways to gain most profit and avoiding possible risk when it comes to managing a portfolio. Capital at risk is a version of risk measures, which improves drawbacks and provides convenient solutions even under complicated constraints. This article is to define the concept on minimizing capital at risk and discuss specific ways to realize the process.

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In the preliminary section, it introduces the definitions and theorems for solving equations, which includes the stochastic processes and the simple and multi dimensional Black-Scholes model. Then, the following section defines and proves the properties of wealth process. Next, it defines Capital-at-Risk (CaR) and give numerical examples to support the definition. After that, it discusses CaR Minimization and condition under Correlation Constraint. Finally, the article focuses on the pricing Kernel Inverse as the Benchmark Portfolio, and also discusses risk management during Economic Depression.

The article gives examples and expands proofs. In the section of CaR, the article gives a numerical example in a discrete time version by showing CaR at Different Alpha levels. In the CaR Minimization section, it proves the proposition of solution of the minimum CaR portfolio, following with a numerical example based on binomial trees. Whats more, when it discusses CaR minimization under Correlation Constraint, the article proves the solutions of optimal portfolio and minimization of CaR. It also gives my own two examples considering three stocks scenario. Finally, in the last section of the article, it focuses on the impact of correlation constraint on portfolio diversification by comparing the relative equations of constrained and unconstrained case. Such impact is also tested during period of economic depression.

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