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.
First Speaker: Rüdiger Kiesel (Universität Duisburg-Essen)
Title: Carbon Default Swap -- Disentangling the Exposure to Carbon Risk Through CDS
Abstract: Using Credit Default Swap spreads, we construct and validate a forward-looking, market-implied carbon risk (CR) factor and show that the impact of carbon regulations on firms' credit risk varies with the regulation's scope and stringency, and with the speed of mandated carbon reduction. Explicit carbon pricing sharpens lenders' evaluations, resulting in firms under such regimes incurring three times the additional credit protection costs. This impact escalates with the proportion of a firm’s direct emissions subject to regulation (stringency) and varies by the sector where firms operate. With an increase in the CR factor, lenders foresee higher costs for short-term transitions.
Second Speaker: Carole Bernard (Vrije Universiteit Brussel)
Title: Risk sharing under ambiguity
Abstract: The distribution of future losses related e.g., to climate risk is typically not perfectly known. We investigate how to design an optimal sharing scheme among agents (insurers; reinsurers; countries...). We first derive the optimal risk sharing under mean-variance preferences when there is possibly distributional ambiguity on the risk to be shared. It is shown that proportional risk sharing is always optimal and that the presence of ambiguity does not affect the risk sharing. Several generalizations are investigated.
First Speaker: Gechun Liang (University of Warwick)
Title: Utility maximization in constrained and unbounded financial markets: Applications to indifference valuation, regime switching, consumption and Epstein-Zin recursive utility
Abstract: This talk presents a systematic study of utility maximization problems for an investor in constrained and unbounded financial markets. Building upon the foundational work of Hu et al. (2005) [Ann. Appl. Probab.15, 1691--1712] in a bounded framework, we extend our analysis to more challenging unbounded cases. Our methodology combines quadratic backward stochastic differential equations with unbounded solutions and convex duality methods. Central to our approach is the verification of the finite entropy condition, which plays a pivotal role in solving the underlying utility maximization problems and establishing the martingale property and convex duality representation of the value processes. Through four distinct applications, we first study utility indifference valuation of financial derivatives with unbounded payoffs, uncovering novel asymptotic behavior as the risk aversion parameter approaches zero or infinity. Furthermore, we study the regime switching market model with unbounded random endowments and consumption-investment problems with unbounded random endowments, both constrained to portfolios chosen from a convex and closed set. Finally, we investigate investment-consumption problems involving an investor with Epstein-Zin recursive utility in an unbounded financial market.
Second Speaker: Dirk Becherer (Humboldt-Universität zu Berlin)
Title: Common Noise by Random Measures: Mean-Field Equilibria for Competitive Investment and Hedging
Abstract: We study mean-field games where common noise dynamics are described by integer-valued random measures, for instance Poisson random measures, in addition to Brownian motions. In such a framework, we describe Nash equilibria for mean-field portfolio games of both optimal investment and hedging under relative performance concerns with respect to exponential (CARA) utility preferences. Agents have independent individual risk aversions, competition weights and initial capital endowments, whereas their liabilities are described by contingent claims which can depend on both common and idiosyncratic risk factors. Liabilities may incorporate, e.g., compound Poisson-like jump risks and can only be hedged partially by trading in a common but incomplete financial market, in which prices of risky assets evolve as Itô-processes. Mean-field equilibria are fully characterized by solutions to suitable McKean-Vlasov forward-backward SDEs with jumps, for whose we prove existence and uniqueness of solutions, without restricting competition weights to be small. A novel change of measure argument and one-to-one relation to an auxiliary mean field game play key roles for proof, helping among other things to avoid restrictive conditions for an approach by direct fixed point contraction.
First Speaker: John Armstrong (King´s College London)
Title: Optimal risk-sharing in collective pension funds
Abstract: The first collective defined contribution (CDC) scheme in the UK opened in October 2024. We will examine its design through the lens of financial mathematics, and in particular will see how the use of approximate discounting formulae rather than risk-neutral pricing leads to surprisingly large, undesirable intergenerational cross subsisidies in this design. We will examine a simple alternative design, founded directly in financial mathematics theories which yields provably optimal results in complete markets and will discuss how this design might be extended in incomplete markets. We will focus on the example of insuring against longevity risk, solving the associated optimal control problems for homogeneous funds, and examining the potential benefits of mutual insurance against systematic longevity risk in inhomogeneous funds.
Second Speaker: Michalis Anthropelos’ (University of Piraeus)
Title: Continuous-time Equilibrium Returns in Markets with Price Impact and Transaction Costs
Abstract: We consider an Itô-financial market at which the risky assets' returns are derived endogenously through a market-clearing condition amongst heterogeneous risk-averse investors with quadratic preferences and random endowments. Investors act strategically by taking into account the impact that their orders have on the assets' drift. A frictionless market and an one with quadratic transaction costs are analysed and compared. In the former, we derive the unique Nash equilibrium at which investors' demand processes reveal different hedging needs than their true ones, resulting in a deviation of the Nash equilibrium from its competitive counterpart. Under price impact and transaction costs, we characterize the Nash equilibrium through the (unique) solution of a system of FBSDEs and derive its closed-form expression. We furthermore show that under common risk aversion and absence of noise traders, transaction costs do not change the equilibrium returns. On the contrary, when noise traders are present, the effect of transaction costs on equilibrium returns is amplified due to price impact.