Mathematical Finance
Research focus
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1. Stochastic calculus of variations, application to mathematical finance [J6, BC9]. Malliavin calculus can be used to derive hedging strategies in a general framework (non Black- Scholes world). The approach is also useful reduce variance in Monte Carlo method applications and therefore to increase its convergence speed. 2. No arbitrage pricing of exotic options and in incomplete markets [J11, J12, J13]. A closed form solution to no arbitrage pricing problems can be obtained only for some specific contingent claim payoffs (e.g. call options) with asset prices evolving according to simple stochastic processes/complete markets (lognormal process). Exotic options are characterized by complex payoffs, i.e., typically the contingent claim payoff is a function of the asset price path. For these contracts it is difficult to find out a closed form solution for the derivative price. In an incomplete market setting, the asset price is influenced by more than one risk component, e.g., stochastic volatility, jumps, etc.. In this setting no arbitrage pricing tools involve many technical difficulties. These two frameworks represent the frontier of option pricing both on the theoretical perspective and on the practical side. 3. Financial market models [J3, J4, J7]. There is a large and growing literature aiming to model asset price evolution in a realistic way. The literature, named financial market microstructure, includes sophisticated economic and mathematical tools such as filtering, stochastic optimisation, equilibrium analysis with incomplete information, game theory. 4. Corporate finance/governance [J5, J8, B10]. After some recent financial scandals, there is a strong attention by financial authorities to the company corporate governance. The topic is qualitative but there are attempts to model the phenomenon mathematically and to analyse it from a quantitative point of view (empirically through econometric/statistic methods).
Dipartimento di afferenza
Docenti afferenti
Full Professors
Barucci Emilio
Assistant Professors
Sgarra Carlo