Das Institut für Mathematische Wirtschaftsforschung veranstaltet im Rahmen des Bielefeld Stochastic Afternoon regelmäßig Seminare zum Thema Finanzmathematik. Das Programm des aktuellen Semesters finden Sie hier.
Max Reppen (Boston University)
Titel: Discrete dividends in continuous time: random profitability
Abstract: Optimal dividend problems are concerned with optimizing the dividends of a firm until the time at which its assets are exhausted (so-called ruin/bankruptcy). These problems derive from ruin theory in actuarial science, but have gained interest in corporate finance as a means for understanding capital allocation and firm valuation. We study a dividend problem in which the profitability of the firm is driven by a random process and the firm has the possibility to issue equity at a fixed or proportional cost. In the literature, dividend problems are modeled either in continuous time with continuous control or in discrete time. In our case, the dividend payouts are restricted to discrete time, but other control decisions may be chosen continuously.
Mike Ludkovski (University of California Santa Barbara)
Titel: An Impulse--Regime Switching Game Model of Vertical Competition
Abstract: I will discuss a new kind of non-zero-sum stochastic differential game with mixed impulse/switching controls, motivated by strategic competition in commodity markets. A representative upstream firm produces a commodity that is used by a representative downstream firm to produce a final consumption good. Both firms can influence the price of the commodity. By shutting down or increasing generation capacities, the upstream firm influences the price with impulses. By switching (or not) to a substitute, the downstream firm influences the drift of the commodity price process. We study the resulting impulse--regime switching game between the two firms, focusing on explicit threshold-type equilibria. Remarkably, this class of games naturally gives rise to multiple Nash equilibria, which we obtain via a verification based approach. We exhibit three types of equilibria depending on the ultimate number of switches by the downstream firm (zero, one or an infinite number of switches). We illustrate the diversification effect provided by vertical integration in the specific case of the crude oil market. Our analysis shows that the diversification gains strongly depend on the pass-through from the crude price to the gasoline price. This is joint work with Rene Aid (Paris Dauphine), Luciano Campi (Milano) and Liangchen Li (UCSB, JP Morgan).
Giulia di Nunno (University of Oslo)
Title: Stochastic control for Volterra equations driven by time-changed noises
Abstract: We study a classical control problem for non classical forward dynamics of Volterra type driven by time-changed Levy noises. We consider time-changes that are the abso- lutely continuous type, thus exiting the framework of actual Levy framework. For this we shall consider different information flows and, when necessary, consider these flows either as enlarged filtrations or as partial information. Being the system possibly non- Markovian, we prove stochastic maximum principles of both Pontryagin and Mangasarian type. For this we shall study backward Volterra integral equations with time-change. We illustrate our results with an application to mean-variance portfolio selection.
Johannes Muhle-Karbe (Imperial College London)
Title: Asset Pricing with Frictions
Abstract: We study how equilibrium asset prices depend on “liquidity”, that is, the ease with which the assets can be traded. This leads to fully-coupled systems of coupled forward-backward SDEs. This talk outlines some first wellposedness results, connections to homogenization that lead to the tractable approximations in the large-liquidity limit, and a wide range of challenging open problems in this context.
(Based on joint works (in progress) with Agostino Capponi, Lukas Gonon, Martin Herdegen, Dylan Possamai, Xiaofei Shi and Chen Yang.)
Mogens Steffensen (University of Copenhagen)
Titel: Epiphanies in Pension Investments and Valuation
Abstract: We discuss, on a principle rather than a technical ground, three instances where things are perhaps not the way you thought they were - with potential impact, theoretically or practically. a) In life-cycle portfolio choice, does one really need to take realized capital gains into account, or are age-based investment rules doing the job? b) In time-consistent mean-variance portfolio optimization, is normalization of the variance by current wealth really the 'right' thing to do, or is there a 'better' normalization? c) In multi-state models frequently used in life insurance and credit risk, does there exist such a thing as a set of forward transition rates?
Daniel Bauer (University of Wisconsin-Madison)
Titel: Mortality Risk, Insurance, and the Value of Life (with Darius Lakdawalla and Julian Reif)
Abstract: We develop a new framework for valuing health and longevity improvements that departs from conventional but unrealistic assumptions of full annuitization and deterministic health. Our framework can value the prevention of mortality and of illness, and it can quantify the effects of retirement policies on the value of life. We apply the framework to life-cycle data and generate new insights absent from the conventional approach. First, treatment is up to five times more valuable than prevention, even when both extend life equally. This asymmetry helps explain low observed investment in preventive care. Second, severe illness can significantly increase the value of statistical life, helping to reconcile theory with empirical findings that consumers value life-extension more in bleaker health states. Third, retirement annuities boost aggregate demand for life-extension. We calculate that Social Security adds $10.6 trillion (11 percent) to the value of post-1940 longevity gains and would add $127 billion to the value of a one percent decline in future mortality.