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We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete.…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…
Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work (2004) the…
No-arbitrage asset pricing characterizes valuation through the existence of equivalent martingale measures relative to a filtration and a class of admissible trading strategies. In practice, pricing is performed across multiple asset…
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…
In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution…
Although the valuation of life contingent assets has been thoroughly investigated under the framework of mathematical statistics, little financial economics research pays attention to the pricing of these assets in a non-arbitrage, complete…
We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets…
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the…
I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect…
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically…
In a seminal paper, F. Delbaen and W. Schachermayer proved that the classical NA ("no arbitrage") condition implies the existence of an "absolutely continuous local martingale measure" (ACLMM). It is known that in general the existence of…
Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi\'c and Urusov (2012c)…
Financial models do not merely analyse markets, but actively shape them. This effect, known as performativity, describes how financial theories and the subsequent actions based on them influence market processes, by creating self-fulfilling…
We use the martingale method to discuss the relationship between mean-variance (MV) and monotone mean-variance (MMV) portfolio selections. We propose a unified framework to discuss the relationship in general financial markets without any…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage…
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these…