This paper proposes methods for obtaining risk neutral distributions when only the statistical density is observed. We employ renormalized exponential tilts and estimate the tilt coefficients from related options markets. Particular emphasis is placed on reinsurance losses for which we price in...

This paper proposes an aggregate deposit insurance premium design that is risk-based in the sense that the premium structure ensures the deposit insurance system has a target of survival over the longer term. Such a premium system naturally exceeds the actuarily fair value and leads to a growth...

Complex insurance risks typically have multiple exposures. Options on multiple underliers with a short maturity are employed to hedge this exposure. Hedges are illustrated for GMWBVA accounts invested in the nine sector ETF's of the US economy. The underliers are simulated risk neutrally by...

Financial entities commonly go bankrupt with disastrous consequences for individuals and society These consequences arise since bankrupt limited liability company is not responsible for losses exceeding its financial resources. Such losses are carried by unsecured creditors or, in the case of...

We define the class of local Lévy processes. These are Lévy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded...

Minimal discounted distorted expectations across a range of stress levels are employed to model risk acceptability in markets. Interactions between discounting and stress levels used in measure changes are accommodated by lowering discount rates for the higher stress levels. Acceptability...

Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The...

We define the class of local Lévy processes. These are Lévy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded...

We consider the problem of optimal investment in a risky asset, and in derivatives written on the price process of this asset, when the underlying asset price process is a pure jump Lévy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and...

A Markov chain with an expanding non-uniform grid matching risk neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with prespecified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from...