MATHEMATICAL MODELS FOR FINANCIAL MARKETS

Model prices in the financial markets

The cardinal utility theory; axiomatic structure. fundamental theorem.

Intensity of preference. Absolute and relative risk measures.

The certainty equivalent. Applications equivalent course. Risk premium.

Main families of utility functions and their properties. Paradoxes of Allais and Ellsberg. Some experiments by Kahneman and Tversky .

First and second order stochastic dominance.

Portfolio Theory. Mean-variance models. Risk indices.

Only two risky assets. Efficient Frontier: possible cases particularly interesting.

Contraction risk. Portfolio of minimum risk.

Model mean-variance with the most risky assets.

Main theorems on the efficient frontier. Feasible set and shape of the border.

Diversification and risk reduction. Systematic risk.

Diversification and risk reduction. Systematic risk. Minimization of the variance of the portfolio.

Maximizing the risk premium and the consequences on the efficient frontier. The Chapital Market Line. Portfolio Market. Separation theorem.

CAPM assumptions and mathematical derivations of the model. SML. Systematic risk and specific risk. The coefficient '' beta ''. Diversification and risk reduction in the CAPM.

Non-standard versions of the CAPM.

Single Index Model. Multifactorial models.

Options: first definitions and payoffs. Using options for basic risk management.

Hedging strategies by combining options and below.

The spreads. Combinations of options. Put-call parity. Minimum and maximum limits for the value of a put and a call.

Risk-neutral pricing model.

Fixed-Income Market Models and Derivatives.

1. J. Cvitanic, F. Zapatero, “Introduction to the Economics and Mathematics of Financial Markets.’’The MIT Press Cambridge, Massachusetts London, England, 2004.

2. D. Luenberger , “Finanza e Investimenti’’, Apogeo, Milano 2006.

3. J. Berck , P. DeMarzo, “Chapital budgeting”, Addison Wesley (Pearson International Ed.), Milano 2009.

4. J. Berck, P. DeMarzo, “Finanza aziendale 2”, Addison Wesley (Pearson International Ed.), Milano 2008.

5. S. Benninga , “Modelli finanziari”, McGraw-Hill, Milano 2010.

6. E. J. Elton, M. J. Gruber ,“Modern portfolio theory and investment analysis”, Wiley, 2002.