A target benefit plan (TBP) is a collective defined contribution (DC) plan that is growing in popularity in Canada. Similar to DC plans, TBPs have fixed contribution rates, but they also implement pooling of longevity and investment risk. In this paper, we formulate a multi-period model that incorporates two sources of risk – asset risk and labor income risk for active members. We present an optimal investment and retirement benefits schedule for TBP members with a fixed contribution rate. Using Australian data from 1965 to 2018, we evaluate the performance of the optimal TBP scheme and compare it to the optimal DC scheme. By adopting the benefit–investment strategy derived in this paper, we demonstrate the stability of benefit distribution over time for a TBP scheme in this stochastic formulation. To outperform the DC scheme’s benefit payment, careful consideration shall be given to the benefit target in the TBP scheme. A high target may not be achievable, while a low target can impede the accumulation momentum of the fund’s wealth in its early stages. Moreover, a TBP fund’s investment strategy is primarily influenced by the wealth target, with more aggressive investments in risky assets as the wealth target increases. This analysis may shed light on the possible improvements to retirement planning in Australia. Although the results are sensitive to the choice of model parameters, overall, the proposed TBP promotes system stability in various scenarios.

We study an optimal investment problem under a joint limited expected relative loss and portfolio insurance constraint with a general random benchmark. By making use of a static Lagrangian method in a complete market setting, the optimal wealth and investment strategy can be fully determined along with the existence and uniqueness of the Lagrangian multipliers. Our numerical demonstration for various commonly used random benchmarks shows a trade-off between the portfolio outperformance and underperformance relative to the benchmark, which may not be captured by the widely used Omega ratio and its utility-transformed version, reflecting the impact of the benchmarking loss constraint. Furthermore, we develop a new portfolio performance measurement indicator that incorporates the agent’s utility loss aversion relative to the benchmark via solving an equivalent optimal asset allocation problem with a benchmark-reference-based preference. We show that the expected utility performance is well depicted by looking at this new portfolio performance ratio, suggesting a more suitable portfolio performance measurement under a limited loss constraint relative to a possibly random benchmark.

We study the optimal investment strategy to minimize the probability of lifetime ruin under a general mortality hazard rate. We explore the error between the minimum probability of lifetime ruin and the achieved probability of lifetime ruin if one follows a simple investment strategy inspired by earlier work in this area. We also include numerical examples to illustrate the estimation. We show that the nearly optimal probability of lifetime ruin under the simplified investment strategy is quite close to the original minimum probability of lifetime ruin under reasonable parameter values.

We determine the optimal robust strategy of an individual who seeks to maximize the (penalized) probability of reaching a bequest goal when she is uncertain about the drift of the risky asset and her hazard rate of mortality. We assume the individual can invest in a Black–Scholes market. We solve two optimization problems with ambiguity. The first is to maximize the penalized probability of reaching a bequest goal without life insurance in the market. In the second problem, in addition to investing in the financial market, the individual is allowed to purchase term life insurance to help her reach her bequest goal. As the individual becomes more ambiguity averse concerning the drift of the risky asset, she becomes more conservative with her investment strategy. Also, as she becomes more ambiguity averse about her hazard rate of mortality, numerical work indicates she is more likely to buy life insurance when the ambiguity towards the return of the risky asset is not too large.

We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.

In a defaultable market, an investor trades having only partial information about the behavior of the market. Taking into account the intraday stock movements, the risky asset prices are modelled by marked point processes. Their dynamics depend on an unobservable process, representing the amount of news reaching the market. This is a marked point process, which may have common jump times with the risky asset price processes. The problem of hedging a defaultable claim is studied. In order to discuss all these topics, in this paper we examine stochastic control problems using backward stochastic differential equations (BSDEs) and filtering techniques. The goal of this paper is to construct a sequence of functions converging to the value function, each of these is the unique solution of a suitable BSDE.

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.

We study the continuous-time portfolio optimization problem of an insurer. The wealth of the insurer is given by a classical risk process plus gains from trading in a risky asset, modelled by a geometric Brownian motion. The insurer is not only interested in maximizing the expected utility of wealth but is also concerned about the ruin probability. We thus investigate the problem of optimizing the expected utility for a bounded ruin probability. The corresponding optimal strategy in various special classes of possible investment strategies will be calculated. For means of comparison we also calculate the related mean-variance optimal strategies.

This paper analyzes optimal investment policies for pension funds of a defined benefit (DB) type. The nature of a DB fund induces a natural modeling of preferences being of the mean-downside risk type. With compensation for inflation as an explicit goal of a pension fund, a natural reference point for the risk measure is the future (indexed) value of the liabilities. Results are presented for different levels of inflation uncertainty and its correlation with stock returns. The optimal decision rules show increased risk-taking for funding ratios moving away from the discounted value of the reference point. Furthermore, it is shown that the outcomes are comparable with those using a mean-downside deviation criterion. We provide intuition for the results and compare the outcomes with actual investment policies of six large Dutch pension funds.