2024 London Mathematical Finance Seminar Series
Autumn 2024 (Oct-Dec) @ King's College London
Date:
Thursday, October 10, 2024
Time: 16:00-17:00
Location:
Room
FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
John Armstrong (King's College London)
Title: Rough paths and gamma hedging
Abstract: We will show how the gamma-hedging trading strategy natural emerges from the theory of rough paths. Since rough-path theory is non-probabilistic, this gives sure convergence results for the discrete-time gamma-hedging strategy that depend only on the regularity of the signal. As an example, we show that European options can be replicated using the gamma-hedging strategy so long as the stock price process and the implied volatility process of the hedging option are sufficiently regular, but without any probabilistic assumptions on the signal. We will examine how these results generalize to path-dependent options.
Date: Thursday, October 10, 2024
Time: 17:00-18:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
Seyoung Park (Nottingham University Business School)
Title: Income Disaster Model with Optimal Consumption
Abstract: We propose a continuous-time income disaster model with optimal consumption. We endogenously determine the stochastic discount factor (SDF) in an incomplete market caused by income disaster. We then derive optimal consumption decisions for two types of agents, one who is exposed to income disaster and another who is not. We find a large incomplete-markets precautionary savings term between the two agents, which pushes the interest rate down and helps to resolve the risk-free rate puzzle. Interestingly, with income disaster the equilibrium interest rate is a decreasing function of risk aversion while the equity premium is an increasing function. Finally, our model can better match empirical marginal propensities to consume numbers and explain the low-consumption-high-savings puzzle.
Date: Thursday, October 24, 2024
Time: 16:00-17:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
Moris Strub (Warwick Business School)
Title: How to Choose a Model? A Consequentialist Approach Applied to Portfolio Selection in Continuous-Time
Abstract: We propose a consequentialist approach to model selection: Models should be chosen not according to statistical criteria, but in view of how they are used. This principle is then studied in detail for continuous-time portfolio choice. Specifically, we consider an econometrician with prior beliefs on the likelihood of models to transpire and faced with the task of communicating a single model to a client. The client then accepts the model communicated by the econometrician and invests according to the strategy that maximizes expected utility within this specific model. As a consequence, the client receives the consequential performance of trading according to the model communicated by the econometrician in a potentially different model which accurately describes the world. The objective of the econometrician is to choose the model that maximizes the consequential performance of the client, averaged over the likelihood of models to transpire and weighted according to the risk preferences of the econometrician. One of the key findings is that it is best to recommend a model that is more optimistic than an unbiased estimator would suggest. This presentation is based on joint work with Thaleia Zariphopoulou.
Date: Thursday, October 24, 2024
Time: 17:00-18:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
Dylan Possamaï (ETH Zürich)
Title: A target approach to Stackelberg games
Abstract: In this paper, we provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a Stackelberg game in which the leader and the follower can both control the drift and the volatility of a stochastic output process, in order to maximise their respective expected utility. The aim is to characterise the Stackelberg equilibrium when the players adopt "closed-loop strategies", i.e. their decisions are based solely on the historical information of the output process, excluding especially any direct dependence on the underlying driving noise, often unobservable in real-world applications. We first show that, by considering the-second-order-backward stochastic differential equation associated with the continuation utility of the follower as a controlled state variable for the leader, the latter's unconventional optimisation problem can be reformulated as a more standard stochastic control problem with stochastic target constraints. Thereafter, adapting the methodology developed by Soner and Touzi or Bouchard, Élie, and Imbert, the optimal strategies, as well as the corresponding value of the Stackelberg equilibrium, can be characterised through the solution of a well-specified system of Hamilton–Jacobi–Bellman equations. For a more comprehensive insight, we illustrate our approach through a simple example, facilitating both theoretical and numerical detailed comparisons with the solutions under different information structures studied in the literature. This is a joint work with Camilo Hernández, Nicolás Hernández Santibáñez, and Emma Hubert.
Date: Thursday, November 7, 2024
Time: 16:00-17:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Nicole Baeuerle (Karlsruhe Institute of Technology)
Title: Optimal investment in ambiguous financial markets with learning
Abstract: We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff, Marinacci and Mukerji, 2005) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a driftdistribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. We rely on some duality theorems to prove our statements. Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution. We illustrate our findings with a numerical study. If time allows we will briefly discuss how these ideas can be used for other stochastic dynamic optimization problems.
The talk is based on a joint work with Antje Mahayni.
Date: Thursday, November 7, 2024
Time: 17:00-18:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Hirbod Assa (University of Essex)
Title: Systematic Risk in Pools
Abstract: In the realm of portfolio diversification, the focus lies on constructing a well-diversified portfolio to mitigate unsystematic risk, allowing for the identification and measurement of systematic risk through uni-factor, CAPM, and multi-factor, APT, models. This approach is rooted in the belief that, with a sufficiently diversified portfolio, unsystematic risk in theory can be eliminated, making the remaining systematic risk more apparent. While diversification is the mean to diversify the unsystematic risk in a portfolio management problem, pooling strategies, with a limited strategy of just expanding the pool members, necessitate a distinct approach to systematic risk. In such scenarios, the challenge lies in disentangling the impact of systematic factors from idiosyncratic influences within a pool. This paper explores the methodologies and considerations unique to pooling situations, shedding light on the complexities involved in identifying and quantifying systematic risk in a pool. In our effort to assess the concept of systematic risk in a pool, we adopt an approach that identifies the defining characteristics of systematic risks, which remain invariant regardless of the number of losses or any manipulations within a finite set of losses. To explore these principles, we find a framework of risk management on sequences in Banach lattices to be particularly suitable. In establishing these principles, we introduce the notion of “systematic compatibility”, signifying invariance to variations in finite changes within a sequence of losses. Consequently, we observe that while systematic risk often possesses an implicit representation in the risk space, it exhibits an explicit representation in the bi-dual space. Moreover, we introduce systematic compatible risk measures and establish their dual characterization. We demonstrate that risk measurement can naturally be represented as a split into a summation of systematic and unsystematic components. In practical applications, we employ these measures to address risk management problems, with a specific emphasis on risk pooling scenarios. In revisiting the traditional “principle of insurance” (POI), we propose an extension called the “principle of pooling” (POP). By showing that the principle of pooling holds if and only if the systematic risk is secure, we investigate this novel concept.
Date: Thursday, November 21, 2024
Time: 16:00-17:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Mathias Beiglböck (University of Vienna)
Title: Non-linear transport theory and applications in finance.
Abstract:
Gozlan, Roberto, Samson and Tetali introduced a non-linear relaxation of classical optimal
transport. On the one hand, this framework of weak optimal transport (WOT) still retains many characteristics of usual optimal transport, allowing for a compelling theory. On the other hand, this type of relaxation is suitable to cover a number of problems that lie outside the scope of the classical theory. We give a gentle introduction and discuss the applications to a number of challenges appearing in mathematical finance: this concerns the Bass local volatility model, pricing of VIX futures, robust pricing for fixed income markets and the optimal Skorokhod embedding problem.
Date: Thursday, November 21, 2024
Time: 17:00-18:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Tiziano De Angelis (University of Torino)
Title: Linear-quadratic stochastic control with state constraints on finite-time horizon
Abstract: We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal D\subseteq [0,T]\times\mathbb R^d$, a diffusion $X$ in $\mathbb R^d$ must be linearly controlled in order to keep the time-space process $(t,X_t)$ inside the set $\mathcal D^c:=([0,T]\times\mathbb R^d)\setminus\mathcal D$, while at the same time minimising an expected cost that depends on the state $(t,X_t)$ and it is quadratic in the speed of the control exerted.
We find an explicit probabilistic representation for the value function and the optimal control under a set of mild sufficient conditions concerning the coefficients of the underlying dynamics and the regularity of the set $\mathcal D^c$. Fully explicit formulae are presented in some relevant examples. (Joint work with Erik Ekström, University of Uppsala, Sweden).
Date: Thursday, December 5, 2024
Time: 16:00-17:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Nils Detering (Heinrich Heine University Düsseldorf)
Title: TBA
Abstract: TBA
Date: Thursday, December 5, 2024
Time: 17:00-18:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Claudia Ceci (University of Rome – La Sapienza)
Title: TBA
Abstract: TBA
Date: Thursday, December 12, 2024
Time: 17:00-18:00
Location: Room
CLM.3.02, LSE (Clement House, Aldwych)
Speaker:
Philip Protter (Columbia University)
Title: TBA
Abstract: TBA
