Peter Hieber

University of Lausanne | UNIL ·  Département de sciences actuarielles (DSA)

This paper considers the valuation of equity-linked life insurance contracts that offer an annually guaranteed minimum return. The policy premiums are invested in a reference portfolio that is modeled by means of a regime switching Lévy process where the model parameters depend on a continuous, finite state Markov chain. Thereby, we can take into a...

We study a problem of non-concave utility maximization under a fair pricing constraint. The framework finds many applications in, for example, the optimal design of managerial compensation or equity-linked life insurance contracts. Deriving closed-form solutions, we observe that the fair pricing constraint will reduce the riskiness of the optimal s...

For insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, a...

Many empirical studies confirm that policyholder’s subjective mortality beliefs deviate from the information given by publicly available mortality tables. In this study, we look at the effect of subjective mortality beliefs on the perceived attractiveness of retirement products, focusing on two extreme products, conventional annuities (where the in...

Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent co...

Survivor funds are financial arrangements where participants agree to share the proceeds of a collective investment pool in a predescribed way depending on their survival. This offers investors a way to benefit from mortality credits, boosting financial returns. Following Denuit (2019, ASTIN Bulletin , 49 , 591–617), participants are assumed to ado...

The tendency of insurance providers to refrain from offering long-term guarantees on investment or mortality risk has shifted attention to mutual risk pooling schemes like (modern) tontines, pooled annuities or group self annuitization schemes. While the literature has focused on mortality risk pooling schemes, this paper builds on the advantage of...

In many countries, the decline in interest rates has reduced the interest in traditional participating life insurance contracts with investment guarantees and has led to a shift to unit-linked policies without guarantees. We design a novel mixed insurance contract splitting premium payments between a participating and a unit-linked fund. An additio...

Many empirical studies confirm that policyholder's subjective mortality beliefs deviate from the information given by publicly available mortality tables. In this study, we look at the effect of subjective mortality beliefs on the perceived attractiveness of retirement products, focusing on two extreme products, conventional annuities (where the in...

In Europe, the introduction of the regulatory scheme Solvency II wants to improve the risk management practice in insurance undertakings. One aspect of the new regulatory rules is an improved supervision of distressed insurance undertakings. In case the insurance undertaking is in financial distress, the regulator may force it to take appropriate p...

We study a problem of non-concave utility maximization under a fair pricing constraint. The framework finds many applications in, for example, the optimal design of managerial compensation or equity-linked life insurance contracts. Deriving closed-form solutions , we observe that the fair pricing constraint will reduce the riskiness of the optimal...

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options...

This article considers the valuation of digital, barrier, and lookback options in a Markovian, regime-switching, Black–Scholes model. In Fourier space, integral representations for the option prices are derived via the theory on matrix Wiener–Hopf factorizations. Our main focus is on the 2-state case where the matrix Wiener–Hopf factorization is av...

In a typical equity-linked life insurance contract, the insurance company is entitled to a share of return surpluses as compensation for the return guarantee granted to the policyholders. The set of possible contract terms might, however, be restricted by a regulatory default constraint - a fact that can force the two parties to initiate sub-optima...

We analyze the effects of a prevailing low interest rates regime on investment decisions of insurance companies and on the risk/return profile of participating life insurance policies with different contractually guaranteed minimum annual return. Our analysis is based on German legislation and a stylized insurance company with two cohorts of insure...

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2- and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is up to the roots of a...

Imposing a symmetry condition on returns, Carr and Lee [2009] show that (double) barrier derivatives can be replicated by a portfolio of European options and can thus be priced using fast Fourier techniques (FFT). We show that prices of barrier derivatives in stochastic volatility models can alternatively be represented by rapidly converging series...

Guo (2001a) derived the Laplace transform of the first-passage time in a 2-state Markov-switching model and gave one of the pioneering works improving the analytical tractability of Markov-switching models. However, the Laplace transforms in her paper are wrong. This short note provides the correct expression and an alternative proof using the matr...

Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Mon...

Apart from heteronomy exit events like, e.g., credit default or death, several financial agreements allow policy holders to voluntarily terminate the contract. Examples include callable mortgages or life insurance contracts. For the contractual counterpart, the result is a cash-flow uncertainty called prepayment risk. Despite the high relevance of...

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, e.g., for the pricing of single- and double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model...

Using a unique proprietary data set of 460 realized buyouts completed between 1990 and 2005, we examine the risk appetite of private equity (PE) sponsors in different states of the PE market and analyse key determinants of deal-level equity risk. We develop a new approach to mathematically model PE investment equity risk based on the Black-Cox defa...

For risky investments, like private equity or hedge funds, default risk plays a prominent role. However, the accordant literature on portfolio optimization mostly disregards default risk and accordingly skewed return distributions. This paper presents a realistic and tractable framework for a portfolio optimization including default risk. Default i...

An efficient Monte Carlo simulation for the pricing of barrier options in a Markov-switching model is presented. Compared to a brute-force approach, relying on the simulation of discretized trajectories, the presented algorithm simulates the underlying stock price process only at state changes and at maturity. Given these pieces of information, opt...