Abstract: We document a new empirical fact: the level of cash holdings is U-shaped in firm size. To rationalize this finding, we develop a model of firm dynamics with costly financing that is not homothetic in firm size. Cash levels are U-shaped in firm size due to the interplay of investment and hedging incentives. When a firm is small, cash levels decrease with size because the firm uses cash to grow, capitalizing on better investment opportunities. As the firm grows, investing slows and cash levels eventually increase to hedge larger-scale cash flow shocks. Relatedly, equity issuances are U-shaped in firm size.
This is a joint work with Ali Kakbod, Max Reppen, and Tarik Umar.
Speaker: Igor Cialenco (Illinois Institute of Technology)
Title: SPDEs in finance and their statistical inference
Abstract: In recent years, stochastic partial differential equations (SPDEs) have gained significant traction as a conventional modeling tool in finance. We will start with an overview of several SPDEs based models employed within finance. Subsequently, we will focus on a fast-developing field of statistical inference of these equations. Unlike traditional finite-dimensional stochastic differential equations, statistical models driven by SPDEs are predominantly singular, and hence, conventional inference tools are inadequate and special methods must be developed. We will explore cutting-edge methodologies in estimating some of the parameters entering parabolic SPDEs, discuss methods of proofs of asymptotic properties of these estimators, and conclude with some open problems.
Title: Robust Optimal Growth from an analytical and learning perspective
Abstract: Robust Optimization of Growth is an important but demanding task. Following seminal work of Kostas Kardaras and Scott Robertson we could show that their results, namely that robust growth optimal portfolios are functionally generated, also hold in the presence of stochastic factors. The stochastic factors can be interpreted as actual economic factors or as factors driving model uncertainty. All these insights are applied to facilitate robust learning algorithms. (joint work with David Itkin, Benedikt Koch and Martin Larsson, and with Florian Krach and Hanna Wutte, respectively).
Title: Speeding up the Euler scheme for killed diffusions
Abstract: Let X be a linear diffusion taking values in (l,r) and consider the standard Euler scheme to compute an approximation to E[g(X(T);T<U]] for a given function g and a deterministic T, where U is the first time that X exits (l.r). It is well-known that the presence of killing introduces a loss of accuracy. We introduce a drift-implicit Euler method to bring the convergence rate back to the optimal rate that can be obtained in the absence of killing, using the theory of recurrent transformations developed recently. Numerical experiments concerning barrier options with some notable local volatility models will be presented. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions.
Title: Superhedging duality for multi-action options under model uncertainty with information delay
Abstract: We consider the superhedging price of an exotic option under nondominated model uncertainty in discrete time in which the option buyer chooses some action from an (uncountable) action space at each time step. By introducing an enlarged space, we reformulate the superhedging problem for such an exotic option as a problem for a European option, which enables us to prove the pricing-hedging duality. Next, we present a duality result that, when the option buyer’s action is observed by the seller up to k periods later, the superhedging price equals the model-based price where the option buyer has the power to look into the future for k-periods.
Title: Portfolio choice under taxation and expected market time constraint
Abstract: We consider the problem of choosing an investment strategy that will maximise utility over distributions, under capital gains tax and constraints on the expected liquidation date. We show that the problem can be decomposed in two separate ones. The first involves choosing an optimal target distribution, while the second involves optimally realising this distribution via an investment strategy and stopping time. The latter step may be regarded as a variant of the Skorokhod embedding problem. A solution is given very precisely in terms of the first time that the wealth of the growth optimal portfolio, properly taxed, crosses a moving stochastic (depending on its minimum-to-date) level. The suggested solution has the additional optimality property of stochastically minimising maximal losses over the investment period.
Title: Fractional forward variance models – volatility surfaces and other features
Abstract: We present some features of a class of forward variance models embedding rough volatility models (the archetypal example being the so-called rough Bergomi model): the structure of model-generated VIX smiles, the shapes of model-generated volatility surfaces on the spot price, both implied and local, with a focus on the at-the-money volatility skew, and the ability of such models to capture this specific feature of market Equity data over different time horizons. We present related numerical methods for option pricing and their efficiency, from Monte Carlo to asymptotic methods. If time permits, we will discuss some dynamic properties of such models, looking at the dynamics of implied volatilities they generate.
Title: Moral hazard for time-inconsistent agents, BSVIEs and stochastic targets
Abstract: We address the problem of Moral Hazard in continuous time between a Principal and an Agent that has time-inconsistent preferences. Building upon previous results on non-Markovian time-inconsistent control for sophisticated agents, we are able to reduce the problem of the principal to a novel class of control problems, whose structure is intimately linked to the representation of the problem of the Agent via a so-called extended Backward Stochastic Volterra Integral equation. We will present some results on the characterization of the solution to problem for different specifications of preferences for both the Principal and the Agent, and relate the general setting to control problems with Volterra stochastic target constraints.
Speaker: Antoine Jacquier (Imperial College London)
Title: Quantum algorithms in Finance
Abstract: We introduce several algorithms from Quantum Computing technologies aimed at providing speedup compared to their classical counterparts. We shall highlight in particular how quantum entanglement provides potential expressive explanatory power for neural networks. Time permitting, we will showcase further applications to linear systems and PDEs and to optimisation problems.