Value-at-risk (VaR) and conditional value-at-risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of a Neyman-Pearson type binary solution. We add a constraint on expected return to investigate...

For pension-savers, a low payoff is a financial disaster. Such investors will most likely prefer left-skewed payoff distributions over right-skewed payoff distributions. We explore how such distributions can be delivered. Cautious-relaxed utility measures are cautious in ensuring that payoffs...

Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection,...

Mean-variance portfolio optimization is more popular than optimization procedures that employ downside risk measures such as the semivariance, despite the latter being more in line with the preferences of a rational investor. We describe strengths and weaknesses of semivariance and how to...

We study risk-minimization for a large class of insurance contracts. Given that the individual progress in time of visiting an insurance policy's states follows an F-doubly stochastic Markov chain, we describe different state-dependent types of insurance benefits. These cover single payments at...

We review two complementary mixture-based clustering approaches for modeling unobserved heterogeneity in an insurance portfolio: the generalized linear mixed cluster-weighted model (CWM) and mixture-based clustering for an ordered stereotype model (OSM). The latter is for modeling of ordinal...

We study the gap between the state pension provided by the Italian pension system pre-Dini reform and post-Dini reform. The goal is to fill the gap between the old and the new pension by joining a defined contribution pension scheme and adopting an optimal investment strategy that is...

We show how to solve Merton optimal investment stochastic control problem for Hawkesbased models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t)...