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 probability of ruin. Following recent research, we assume that investment strategies have to be determini...

Abstract: Real options approaches can be employed to value the flexibility in the decision-making courses of phased investments. This paper focuses on the two-stage investment problems of venture firms. Firstly, based on the analysis of profit function and real options thinking, stochastic models are proposed to describe the uncertainties of such problems. Then the value function of decision-ma...

We consider a financial market model driven by an Rn-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of n independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optimal investment problems. These include (i) Merton’s portfolio optimization proble...

We consider the problem of optimal investment when agents take into account their relative performance by comparison to their peers. Given N interacting agents, we consider the following optimization problem for agent i, 1 ≤ i ≤ N : sup π∈Ai EUi ( (1− λi)X i T + λi(X π T − X̄ i,π T ) ) , where Ui is the utility function of agent i, π i his portfolio, X i his wealth, X̄ the average wealth of his p...

This paper concerns the problem of optimal investment and consumption with power utility when there is event risk. Events are modelled by transitions in a finite state Markov chain, but unlike traditional regime switching models, changes in regime (i.e. events) may be accompanied by jumps in the asset price at the instant of transition, where the distribution of the jump sizes are conditional o...

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control problems, that we solve by duality method leading to ...

The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices [1, 2]. Such a distribution typically goes through a maximum at a time coined the optimal investment horizon, τ ρ , which defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels o...

Penetration testing, the deliberate search for potential vulnerabilities in a system by using attack techniques, is a relevant tool of information security practitioners. This paper adds penetration testing to the realm of information security investment. Penetration testing is modeled as an information gathering option to reduce uncertainty in a discrete time, finite horizon, player-versus-nat...

We introduce an equity-credit portfolio framework taking into account the structural interaction of market and credit risk, along with their systemic dependencies. We derive an explicit expression for the optimal investment strategy in stocks and credit default swaps (CDSs). We exploit its representation structure and analyze the mechanisms driving the optimal investment decisions. The transmis...

This paper considers co-investment in a supply chain infrastructure using an inter-temporal model. We assume that firms’ capital is essentially the supply chain’s infrastructure. As a result, firms’ policies consist in selecting an optimal level of employment as well as the level of co-investment in the supply chain infrastructure. Several applications and examples are presented and open-loop, ...