Faced with the problem of pricing complex contingent claims, investors seek to make their valuations robust to model uncertainty. We construct a notion of a modeluncertainty-induced utility function and show that model uncertainty increases investors' effective risk aversion. Using this utility...

The prices of derivatives contracts can be used to estimate ‘risk-neutral' probability density functions that give an indication of the weight investors place on different future prices of their underlying assets, were they risk-neutral. In the likely case that investors are risk-averse, this...

The traditional derivation of risk-neutral probability in the binomial option pricing framework used in introductory mathematical finance courses is straightforward, but employs several different concepts and is is not algebraically simple. In order to overcome this drawback of the standard...

Classical measure underpins the foundations of financial derivative pricing, as the classical expectation satisfies the essential principles of replicability (linearity) and no-arbitrage (positivity) required by any reasonable pricing model. Quantum measure extends this by allowing payoffs to be...

Classical measure underpins the foundations of financial derivative pricing, as the classical expectation satisfies the essential principles of replicability (linearity) and no-arbitrage (positivity) required by any reasonable pricing model. Quantum measure extends this by allowing payoffs to be...

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to...

Cumulative prospect theory (CPT) has been proposed as an alternative to expected utility theory to explain irregular behavior by economic agents. CPT comprises two key transformations: one of outcome values and the other of objective probabilities. Risk attitudes are derived from the shapes of...

Suppose populations of economic agents that are parameterized by skewness preference. For stated agents, increasing marginal utility for wealth necessarily is facilitated by a risk premium function that only robustly is parameterized with reference to `relative safety', as opposed to `relative...

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging...