Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM (SoSe 2019)



Dates - May

Monday, 13.05.2019 - 1. Speech

Speaker: Rama Cont, Oxford University

Topic: Rough calculus: pathwise calculus for functionals of irregular paths

Time: 14:15 o'clock

Place: LMU Mathematics Institute, Theresienstraße 39-B (Room B 349)

Description: Hans Foellmer showed that the Ito formula holds pathwise, for functions paths with finite quadratic variation along a sequence of partitions. We build on Foellmer's insight to construct a pathwise calculus for smooth functionals of continuous paths with regularity defined in terms of the p-th variation along a sequence of time partitions for arbitrary large p >0. We construct a pathwise integral, defined as a pointwise limit of compensated Riemann sums and show that it satisfies a change of variable formula and an isometry formula. Results for functions are extended to path-dependent functionals using the concept of vertical derivative of a functional. Finally, we obtain a "signal plus noise" decomposition for regular functionals of paths with strictly increasing p-th variation. Our results apply to sample paths of semi-martingales as well as fractional Brownian motion with arbitrary Hurst parameter H>0.

Based on joint work with: Anna Ananova (Oxford), Henry Chiu (Imperial College London) and Nicholas Perkowski (Humboldt).

Monday, 13.05.2019 - 2. Speech

Speaker: Russell Gerrard, CASS Business School

Topic: An optimal investment strategy for future pension plans

Time: 15:00 o'clock

Place: LMU Mathematics Institute, Theresienstraße 39-B (Room B 349)

Description: Since the work of Merton (1969) the construction of optimal investment portfolios in a time-homogeneous market has been well understood. We review the situation when market parameters are allowed to vary stochastically and apply this to the problem of constructing a pension investment scheme which provides a guaranteed minimum sum on retirement at the expense of imposing an upper limit. We limit ourselves to the accumulation phase, during which payments are made into the fund. The aim of the overall project is to devise pension investment strategies whose behaviour is close to optimal but which present investors with easily explained choices.

Monday, 13.05.2019 - 3. Speech

Speaker: Alessandra Cretarola, Perugia University

Topic: Indifference Pricing of Pure Endowments via BSDEs under Partial Information

Time: 16:00 o'clock

Place: LMU Mathematics Institute, Theresienstraße 39-B (Room B 349)

Description: We investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset and the mortality index dynamics. Since the market is incomplete due to the presence of basis risk, in alternative to arbitrage pricing we use expected utility maximization under exponential preferences as evaluation approach, which leads to the so-called indifference price. Under partial information this methodology requires filtering techniques that can reduce the original control problem to an equivalent problem in complete information. Using stochastic dynamics techniques, we characterize the indifference price of the insurance derivative via the solutions of suitable backward stochastic differential equations.

Dates - June (24.06.2019, Speakers and titles TBD)

Dates - July (15.07.2019, Speakers and titles TBD)