Stochastic Finance: An Introduction in Discrete Time
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in…
Convex measures of risk and trading constraints
The notion of a convex measure of risk is introduced, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and a corresponding extensions of the representation theorem in terms of probability measures on the underlying space of scenarios are proved.
Optimal execution strategies in limit order books with general shape functions
This work builds on the resilience model proposed by Obizhaeva and Wang (2005) but allows for a general shape of the LOB defined via a given density function, and obtains a new closed-form representation for the optimal strategy of a risk-neutral investor.
Robust Preferences and Convex Measures of Risk
We prove robust representation theorems for monetary measures of risk in a situation of uncertainty, where no probability measure is given a priori. They are closely related to a robust extension of…
Optimal Trade Execution under Geometric Brownian Motion in the Almgren and Chriss Framework
With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren–Chriss framework assuming the…
On the Neyman–Pearson problem for law-invariant risk measures and robust utility functionals
- A. Schied
- 13 February 2004
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures.…
TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS
We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of…
Optimal Basket Liquidation for CARA Investors is Deterministic
Abstract We consider the problem faced by an investor who must liquidate a given basket of assets over a finite time horizon. The investor's goal is to maximize the expected utility of the sales…
Optimal investments for risk- and ambiguity-averse preferences: a duality approach
- A. Schied
- EconomicsFinance and Stochastics
- 7 November 2006
This paper studies the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Kramkov and Schachermayer.
Comparative and qualitative robustness for law-invariant risk measures
It is argued here that Hampel’s classical notion of qualitative robustness is not suitable for risk measurement, and a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz spaces is proposed and analyzed.