Math. Finance
About
Financial mathematics concerns with the mathematical formulation and analysis of financial questions, and in the last decades it has become an important research direction both in academics and in the industry. Our research group employs and develops advanced mathematical techniques in order to address timely financial and actuarial problems facing a sound economic foundation. Of particular relevance are problems of dynamic stochastic optimization, models featuring Knightian uncertainty, partial observation, and strategic interaction, that we address through the theory of stochastic control, BSDEs, partial differential equations and semigroups. On the applicative side, we thus deal with problems of optimal consumption choice, strategic and competitive equilibria, (irreversible) investment, optimal dividends, pricing and hedging in commodity markets, as well as with questions arising in the study of risk measures and premium principles.
Selected Pubblications
- M. Burzoni, F. Riedel, M. Soner. Viability and arbitrage under Knightian Uncertainty, Econometrica, 89, No. 3, 2021, 1207–1234.
- P. Beissner, F. Riedel. Equilibria under Knightian Price Uncertainty, Econometrica, 87(1), 2019, 37-64.
- F. Riedel. Optimal Stopping with Multiple Priors, Econometrica 77(3), 2009, 857-908.
- Q. Lin, F. Riedel. Optimal Consumption and Portfolio Choice with Ambiguous Interest Rates and Volatility, Economic Theory, 71, 2021, 1189–1202.
- P. Beissner, Q. Lin, F. Riedel. Dynamically Consistent α-maxmin expected utility, Mathematical Finance, 30, 2020, 1073-1102.
- G. Ferrari. On an Integral Equation for the Free-Boundary of Stochastic, Irreversible Investment Problems, Annals of Applied Probability 25(1), 2015, 150-176.
- T. De Angelis, S. Federico, G. Ferrari, Optimal Boundary Surface for Irreversible Investment with Stochastic Costs, Mathematics of Operations Research 42(4), 2017, 1135-1161.
- T. De Angelis, G. Ferrari, J. Moriarty. Nash Equilibria of Threshold Type for Two-player Nonzero-sum Games of Stopping, Annals of Applied Probability 28(1), 2018, 112-147.
- G. Ferrari. On the Optimal Management of Public Debt: a Singular Stochastic Control Problem, SIAM Journal on Control and Optimization 56(3), 2018, 2036-2073.
- J. Dianetti, G. Ferrari. Nonzero-Sum Submodular Monotone Follower Games: Existence and Approximation of Nash Equilibria, SIAM Journal on Control and Optimization 58(3), 2020, 1257-1288.
- G. Callegaro, C. Ceci, G. Ferrari. Optimal Reduction of Public Debt under Partial Observation of the Economic Growth, Finance and Stochastics 24(4), 2020, 1083-1132.
- J. Dianetti, G. Ferrari, M. Fischer, M. Nendel. Submodular Mean-Field Games: Existence and Approximation of Solutions, Annals of Applied Probability 31(6), 2021, 2538-2566.
- E. Bandini, T. De Angelis, G. Ferrari, F. Gozzi. Optimal Dividend Payout under Stochastic Discounting, forthcoming on Mathematical Finance, 2022+, DOI: 10.1111/mafi.12339.
- M. Nendel and M. Röckner. Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problems, SIAM J. Control Optim. 59 (2021), 4400-4428.
- M. Nendel. Markov chains under nonlinear expectation. Math. Finance 31 (2021), 474-507.
- M. Nendel, M.D. Schmeck, and F. Riedel. A decomposition of general premium principles into risk and deviation. Insurance Math. Econom. 100 (2021), 193-209.