数理金融
Daily leveraged exchange traded funds amplify gains and losses of their underlying benchmark indexes on a daily basis. The result of going long in a daily leveraged ETF for more than one day is less clear. Here, bounds are given for the…
Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the…
The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the…
We expose a simple solution of the consumption-investment problem pair trading. The proof is based on the remark that the HJB equation can be reduced to a linear parabolic equation solvable explicitly.
We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…
We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a…
The goal of this paper is to disentangle the roles of volume and of participation rate in the price response of the market to a sequence of transactions. To do so, we are inspired the methodology introduced in arXiv:1402.1288,…
A minimal stochastic dynamical model of the interbank network is introduced, with linear interactions mediated by an integral of recent variations. Defining stress as the variance over the banks' states, the interaction correction to the…
This is a supplement to the paper "Liquidity based modeling of asset price bubbles via random matching". The supplement is organized as follows. First, we prove Theorem 3.13 in [1] which provides the existence of the dynamical system D…
We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
This paper studies robust forward investment and consumption preferences within a zero-volatility context. Different from previous works, we consider an incomplete financial market model due to general investment portfolio constraints. We…
This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification…
We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European…
We extend the QLBS model by reformulating via considering a large trader whose transactions leave a permanent impact on the evolution of the exchange rate process and therefore affect the price of contingent claims on such processes.…
Quantum computing has recently appeared in the headlines of many scientific and popular publications. In the context of quantitative finance, we provide here an overview of its potential.
We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra…
Given a geometric Levy alpha-stable wealth process, a log-Levy alpha-stable lower bound is constructed for the terminal wealth of a regular investing schedule. Using a transformation, the lower bound is applied to a schedule of withdrawals…
The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations,…