We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful...

Non-life insurance companies most especially, are often faced with the challenge of predicting the number of claims and claim amount to be incurred at any given time. Overcoming such challenges requires examining claim patterns, which assists in premium determination and setting of reserves. The...

A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the...

We consider the expected shortfall of accounting values, or, mathematically speaking, of random variables that are not continuous (i. e. whose cumulative distribution function is not continuous). Acerbi and Tasche show that one has to abandon the conditional expectation in order to maintain...

This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the...

Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in...

This paper outlines a tactical asset allocation (TAA) strategy that takes signals from the credit markets and applies them to the stock market. A power model is built using the Russell 2000 equity index and the Bank of America/Merrill Lynch High Yield B index. This model is then used in a...

The motivation for this paper is to apply a statistical arbitrage technique of pairs trading to high-frequency equity data and compare its profit potential to the standard sampling frequency of daily closing prices. We use a simple trading strategy to evaluate the profit potential of the data...

Traditional portfolio optimization models specify placement of capital as rather irrevocably and fully at risk through investment horizon(s) or continuously. Under this constraint, asset class allocation typically serves as primary mode of diversification, pursuing risk moderation by seeking to...