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Providing a measure of market risk is an important issue for investors and financial institutions. However, the existing models for this purpose are per definition symmetric. The current paper introduces an asymmetric capital asset pricing…

In this note, we consider a general discrete time financial market with proportional transaction costs as in Kabanov and Stricker (2001), Kabanov et al. (2002), Kabanov et al. (2003) and Schachermayer (2004). We provide a dual formulation…

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…

This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…

The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…

This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…

We present a framework to interpret signal temporal logic (STL) formulas over discrete-time stochastic processes in terms of the induced risk. Each realization of a stochastic process either satisfies or violates an STL formula. In fact, we…

Kusuoka [ Limit Theorem on Option Replication Cost with Transaction Costs, Ann. Appl. Probab. 5, 198--221, (1995).] showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset…

We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of [Kabanov, Y., Hedging and…

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to…

We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…

Motivated by recent work on monotone additive statistics and questions regarding optimal risk sharing for return-based risk measures, we investigate the existence, structure, and applications of Meyer risk measures. Those are monetary risk…

We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case…

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…

The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an…

We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or…

We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…

Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…

We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…

A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…