The paper considers the option of an investor to invest in a project that generates perpetual cash flows, of which the drift parameter is unobservable. The investor invests in a liquid financial market to partially hedge cash flow risk and estimation risk. We derive two 3-dimensional non-linear...

FinTech makes numerous financial products accessible to common investors but up to now, there is no risk measure method specially customized for common investors instead of financial institutions which are generally too big to fail. This paper develops a hedging-based utility risk measure (HBU)...

We consider a perturbed renewal risk model where the inter-claim times are phase-type distributed and the dividend payment is a step function depending on the current surplus level. We obtain the integro-differential equations with boundary conditions for the moment-generating functions and the...

Under an incomplete market, we develop a utility-based pricing model for equity and contingent convertible bond (CCB) while the straight bond is priced by an equilibrium pricing method. We derive the semi-closed-form solutions of the utility-based prices of equity and CCB and the explicit...

We extend the classical compound Poisson risk model to consider the distribution of the maximum surplus before ruin where the claim sizes depend on inter-claim times via the Farlie-Gumbel-Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for this...

We develop a continuous-time dynamic contracting model where a risk-neutral principal hires a risk-averse agent to manage a project. The project risk is controlled by the principal or agent, and there is a trade-off between risk premium and a value-destroying effect of risk. No-saving selection...

This paper considers a Sparre Andersen model in which the inter-claim times have a phase-type distribution and the premium rate is a step function depending on the current surplus level. We derive the system of piecewise integro-differential equations for the Gerber-Shiu discounted penalty...