The literature on capital allocation is biased towards an asset modeling framework rather than an actuarial framework. The asset modeling framework leads to the proliferation of inappropriate assumptions about the effect of insurance line of business growth on aggregate loss distributions. This...

We consider an insurance company whose risk reserve is given by a Brownian motion with drift and which is able to invest the money into a Black–Scholes financial market. As optimization criteria, we treat mean-variance problems, problems with other risk measures, exponential utility and the...

A spectrum of upper bounds (Qα(X ; p) ae[0,∞] on the (largest) (1-p)-quantile Q(X;p) of an arbitrary random variable X is introduced and shown to be stable and monotonic in α, p, and X , with Q0(X ;p) = Q(X;p). If p is small enough and the distribution of X is regular enough, then Qα(X ; p)...

One of the key components of counterparty credit risk (CCR) measurement is generating scenarios for the evolution of the underlying risk factors, such as interest and exchange rates, equity and commodity prices, and credit spreads. Geometric Brownian Motion (GBM) is a widely used method for...

Credit risk is a critical issue that affects banks and companies on a global scale. Possessing the ability to accurately predict the level of credit risk has the potential to help the lender and borrower. This is achieved by alleviating the number of loans provided to borrowers with poor...

We analyse four stochastic claims reserving methods in terms of their capability to estimate reserve risk and how successful they are at predicting distributions and VaRs of claim developments in particular. Both actual data and hypothetical claim triangles support our results. The...

In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value-at-Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing...

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a...

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...

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented...