Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes

This paper presents a technique to solve the problem where a couple aims to optimize their consumption, investment, and life-insurance purchasing strategies, thereby maximizing their family objective until retirement. Assumed correlated lifetimes of the two wage earners are modeled by using both the copula and common-shock models. Subsequently, closed-form solutions are obtained for determination of the optimal strategies in both the copula and a special case of the common-shock models. As observed, use of the copula model is more advantageous in its provision of closed-form strategies and ability to distinguish mortality impacts. The optimization problem considered herein is investigated under a Markovian setting and solved using the Hamilton–Jacobi–Bellman equation. Numerical examples are also provided to illustrate the utility of the proposed optimization strategy.     

Bringing cost transparency to the life annuity market

The financial industry has recently seen a push away from structured products and towards transparency. The trend is to decompose products, such that customers understand each component as well as its price. Yet the enormous annuity market combining investment and longevity has been almost untouched by this development.We suggest a simple decomposed annuity structure that enables cost transparency and could be linked to any investment fund. It has several attractive features: (i) it works for any heterogeneous group; (ii) participants can leave before death without financial penalty; and (iii) participants have complete freedom over their own investment strategy.     

Two-stage financial risk tolerance assessment using data envelopment analysis

Typical questionnaires administered by financial advisors to assess financial risk tolerance mostly contain stereotypes of people, have seemingly unscientific scoring approaches and often treat risk as a one-dimensional concept. In this work, a mathematical tool was developed to assess relative risk tolerance using Data Envelopment Analysis (DEA). At its core, it is a novel questionnaire that characterizes risk by its four distinct elements: propensity, attitude, capacity, and knowledge. Over 180 individuals were surveyed and their responses were analyzed using the Slacks-based measure type of DEA efficiency model. Results show that the multidimensionality of risk must be considered for complete assessment of risk tolerance. This approach also provides insight into the relationship between risk, its elements and other variables. Specifically, the perception of risk varies by gender as men are generally less risk averse than women. In fact, risk attitude and knowledge scores are consistently lower for women, while there is no statistical difference in their risk capacity and propensity compared to men. The tool can also serve as a “risk calculator” for an appropriate and defensible method to meet legal compliance requirements, known as the “Know Your Client” rule, that exist for Canadian financial institutions and their advisors.     

Data envelopment analysis models of investment funds

This paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return-risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research.     

Arithmetic Brownian motion and real options

We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.     

Operational risk: Emerging markets,sectors and measurement

The role of decision support systems in mitigating operational risks in firms is well established. However, there is a lack of investment in decision support systems in emerging markets, even though inadequate operational risk management is a key cause of discouraging external investment. This has also been exacerbated by insufficient understanding of operational risk in emerging markets, which can be attributed to past operational risk measurement techniques, limited studies on emerging markets and inadequate data.     

Robust investment–reinsurance optimization with multiscale stochastic volatility

This paper investigates the investment and reinsurance problem in the presence of stochastic volatility for an ambiguity-averse insurer (AAI) with a general concave utility function. The AAI concerns about model uncertainty and seeks for an optimal robust decision. We consider a Brownian motion with drift for the surplus of the AAI who invests in a risky asset following a multiscale stochastic volatility (SV) model. We formulate the robust optimal investment and reinsurance problem for a general class of utility functions under a general SV model. Applying perturbation techniques to the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation associated with our problem, we derive an investment–reinsurance strategy that well approximates the optimal strategy of the robust optimization problem under a multiscale SV model. We also provide a practical strategy that requires no tracking of volatility factors. Numerical study is conducted to demonstrate the practical use of theoretical results and to draw economic interpretations from the robust decision rules.     

Hysteresis effects under CIR interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. However, for many decisions revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of Ingersoll and Ross (1992) in two ways. Firstly, we include real options on perpetuities (in addition to zero coupon cash flows). Secondly, we incorporate abandonment or disinvestment as well as investment options, and thus model interest rate hysteresis (parallel to revenue uncertainty in Dixit (1989a)). Under stochastic interest rates, economic hysteresis is found to be significant, even for small sunk costs.     

Uncertainty and stepwise investment

We analyze the optimal investment strategy of a firm that can complete a project either in one stage at a single freely chosen time point or in incremental steps at distinct time points. The presence of economies of scale gives rise to the following trade-off: lumpy investment has a lower total cost, but stepwise investment gives more flexibility by letting the firm choose the timing individually for each stage. Our main question is how uncertainty in market development affects this trade-off. The answer is unambiguous and in contrast with a conventional real-options intuition: higher uncertainty makes the single-stage investment more attractive relative to the more flexible stepwise investment strategy.     

Effects of knowledge spillover on inter-organizational resource sharing decision in collaborative knowledge creation

Collaborative knowledge creation is important for firms to gain new competitive advantages, but knowledge outgoing spillover harms their existing competitive advantages, which puts them into a dilemma when investing R&D resources. This study formalizes and investigates this dilemma using the Stackelberg leader–follower framework. Through our analyses, we find that, (1) current knowledge creation efforts and prior knowledge are substitutable in collaborative knowledge creation, and through controlling the ratio of current knowledge creation efforts to prior knowledge invested, the leader and the follower can gain benefits from collaboration and restrict knowledge outgoing spillover simultaneously; (2) because the leader invests resources first and faces moral hazards, it has the incentives to participate in collaborative knowledge creation only when its benefits from collaborative knowledge creation fruits and knowledge incoming spillover are bigger than those of the follower, and the more moral hazards it confronts, the more it demands; (3) the leader and the follower invest resources at ratios consistent with the benefits and costs the resources bring to them if they can determine the amount, or the collaboration is unstable.