数理金融
We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal…
In a continuous-time Kyle setting, we prove global existence of an equilibrium when the insider faces a terminal trading constraint. We prove that our equilibrium model produces output consistent with several empirical stylized facts such…
We prove the existence of an incomplete Radner equilibrium in a model with exponential investors and an endogenous noise tracker. We analyze a coupled system of ODEs and reduce it to a system of two coupled ODEs in order to establish…
In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time $T$ follows a normal distribution with a given mean and a given variance. In both…
We formulate an infinite-horizon optimal investment and consumption problem, in which an individual forms a habit based on the exponentially weighted average of her past consumption rate, and in which she invests in a Black-Scholes market.…
We study market-to-book ratios of stocks in the context of Stochastic Portfolio Theory. Functionally generated portfolios that depend on auxiliary economic variables other than relative capitalizations ("sizes") are developed in two ways,…
Reinforcement learning (RL) is gaining attention by more and more researchers in quantitative finance as the agent-environment interaction framework is aligned with decision making process in many business problems. Most of the current…
Quadratic hedging of option payoffs generates the variance optimal martingale measure. When an option features an exercise policy and its cash flows are hedged according to this approach, it may be tempting to optimize such a policy under…
There is substantial empirical evidence showing the fundamental portfolio outperforming the market portfolio. Here a theoretical foundation is laid that supports this empirical research. Assuming stock prices revert around fundamental…
In this paper, we consider a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that…
For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt…
In this non-technical introduction to diamond trees and forests, we focus on their application to computation in stochastic volatility models written in forward variance form, rough volatility models in particular.
We present a family of multi-asset automated market makers whose liquidity curves are derived from the financial principles of self financing transactions and rebalancing. The constant product market maker emerges as a special case.
We provide explicit approximation formulas for VIX futures and options in forward variance models, with particular emphasis on the family of so-called Bergomi models: the one-factor Bergomi model [Bergomi, Smile dynamics II, Risk, 2005],…
This article introduces an intrinsic entropy model that can be used as an indicator to gauge investor interest in a given exchange-traded security, along with the state of the general market corroborated by individual security trade data.…
Grasping the historical volatility of stock market indices and accurately estimating are two of the major focuses of those involved in the financial securities industry and derivative instruments pricing. This paper presents the results of…
In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transaction costs. In the Bachelier setting with exponential…
We investigate the approximation of path functionals. In particular, we advocate the use of the Karhunen-Lo\`eve expansion, the continuous analogue of Principal Component Analysis, to extract relevant information from the image of a…
Suppose an investor aims at Delta hedging a European contingent claim $h(S(T))$ in a jump-diffusion model, but incorrectly specifies the stock price's volatility and jump sensitivity, so that any hedging strategy is calculated under a…
We show that pointwise limits of semistatic trading strategies in discrete time are again semistatic strategies. The analysis is carried out in full generality for a two-period model, and under a probabilistic condition for multi-period,…