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We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…
Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that…
We study a continuous-time asset-allocation problem for an insurance firm that backs up liabilities from multiple non-life business lines with underwriting profits and investment income. The insurance risks are captured via a…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
This article develops a model that takes into account skewness risk in risk parity portfolios. In this framework, asset returns are viewed as stochastic processes with jumps or random variables generated by a Gaussian mixture distribution.…
We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This…
The practice of valuation by marking-to-market with current trading prices is seriously flawed. Under leverage the problem is particularly dramatic: due to the concave form of market impact, selling always initially causes the expected…
Protection of creditors is a key objective of financial regulation. Where the protection needs are high, i.e., in banking and insurance, regulatory solvency requirements are an instrument to prevent that creditors incur losses on their…
The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an…
Motivated by the current global high inflation scenario, we aim to discover a dynamic multi-period allocation strategy to optimally outperform a passive benchmark while adhering to a bounded leverage limit. To this end, we formulate an…
We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is…
In this paper, we extend the jump-diffusion model proposed by Davis and Lleo to include jumps in asset prices as well as valuation factors. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive…
This paper investigates the optimal retirement decision, investment, and consumption strategies in a market with jump diffusion, taking into account habit persistence and stock-wage correlation. Our analysis considers multiple stocks and a…
We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…
In this paper we consider the De Finetti's optimal dividend and capital injection problem under a Markov additive model. We assume that the surplus process before dividends and capital injections follows a spectrally positive Markov…
It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work…
The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk…
This paper studies de Finetti's optimal dividend problem with capital injection. We confirm the optimality of a double barrier strategy when the underlying risk model follows a L\'evy process that may have positive and negative jumps. The…
CRRA utility where the risk aversion coefficient is a constant is commonly seen in various economics models. But wealth-driven risk aversion rarely shows up in investor's investment problems. This paper mainly focus on numerical solutions…
Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…