The Bioeconomics of Marine Sanctuaries

Consider an offshore fishing grounds of size K. Suppose the grounds has been overfished to the point that net revenue has been driven to zero and the fishery is in open access equilibrium at (X, Y). A marine sanctuary, where fishing is prohibited, is then created. Suppose the marine sanctuary is of size K₂ and that fishing is allowed on a smaller grounds, now of size K₁, where K₁ + K₂ = K. In the first, deterministic, model, the present value of net revenue from the grounds-sanctuary system is maximized subject to migration (diffusion) of fish from the sanctuary to the grounds. The size of the sanctuary is varied, the system is re-optimized, and the populations levels, harvest, and value of the fishery is compared to the 'no-sanctuary' optimum, and the open access equilibrium. In the deterministic model, a marine sanctuary reduces the present value of the fishery relative to the 'ideal' of optimal management of the original grounds. In the second model net growth is subject to stochastic fluctuation. Simulation demonstrates the ability of a marine sanctuary to reduce the variation in biomass on the fishing grounds. Variance reduction in fishable biomass is examined for different-sized sanctuaries when net growth on the grounds and in the sanctuary fluctuate independently and when they are perfectly correlated. For the stochastic model of this paper, sanctuaries ranging in size from 60 to 40% of the original grounds (0.6 K₂/K 0.4) had the ability to lower variation in fishable biomass compared to the no sanctuary case. For a sanctuary equal to or greater than 70% of the original grounds (K₂ 0.7K), net revenue would be nonpositive and there would be no incentive to fish.     

Valuation of commodity derivatives in a new multi-factor model

This paper extends existing commodity valuation models to allow for stochastic volatility and simultaneous jumps in the spot price and spot volatility. Closed-form valuation formulas for forwards, futures, futures options, geometric Asian options and commodity-linked bonds are obtained using the Heston (1993) and Bakshi and Madan (2000) methodology. Stochastic volatility and jumps do not affect the futures price at a given point in time. However, numerical examples indicate that they play important roles in pricing options on futures. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility

We show that, for three common SARV models, fitting a minimummean square linear filter is equivalent to fitting a GARCH model.This suggests that GARCH models may be useful for filtering,forecasting, and parameter estimation in stochastic volatilitysettings. To investigate, we use simulations to evaluate howthe three SARV models and their associated GARCH filters performunder controlled conditions and then we use daily currency andequity index returns to evaluate how the models perform in arisk management application. Although the GARCH models produceless precise forecasts than the SARV models in the simulations,it is not clear that the performance differences are large enoughto be economically meaningful. Consistent with this view, wefind that the GARCH and SARV models perform comparably in testsof conditional value-at-risk estimates using the actual data.     

Time diversification and security preferences: A stochastic dominance analysis

We use stochastic dominance to test whether investor should prefer riskier securities as the investment horizon lengthens. Return distributions for stocks, bonds, and U.S. Treasury bills are generated for holding periods of one to 25 years by simulation. For each holding period, stochastic dominance tests are run to establish preferences between the alternative security classes. Contrary to previous mean-variance based studies, we find no evidence that high-risk securities (stocks) dominate low-risk securities (bonds, Treasury bills) as the investment horizon lengthens. However, we do find that corporate bonds systematically dominate government bonds.     

Optimal portfolio choice in the bond market

We consider the Merton problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. Working within a Markovian Heath–Jarrow–Morton model of the interest rate term structure driven by an infinite-dimensional Wiener process, we give sufficient conditions for the existence and uniqueness of an optimal trading strategy. When there is uniqueness, we provide a characterization of the optimal portfolio as a sum of mutual funds. Furthermore, we show that a Gauss–Markov random field model proposed by Kennedy [Math. Financ. 4, 247–258(1994)] can be treated in this framework, and explicitly calculate the optimal portfolio. We show that the optimal portfolio in this case can be identified with the discontinuities of a certain function of the market parameters.     

Machine learning in individual claims reserving

Machine learning techniques make it feasible to calculate claims reserves on individual claims data. This paper illustrates how these techniques can be used by providing an explicit example in individual claims reserving.     

Automatic balancing mechanisms for notional defined contribution accounts in the presence of uncertainty

The notional defined contribution model combines pay-as-you-go financing and a defined contribution pension formula. This paper aims to demonstrate the extent to which liquidity and solvency indicators are affected by fluctuations in economic and demographic conditions and to explore the introduction of an automatic balancing mechanism (ABM) into the pension scheme. We demonstrate that the introduction of an ABM reduces the volatility of the buffer fund and that, in most cases, the automatic mechanism that re-establishes solvency produces the highest value of the risk-adjusted notional factor.     

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.     

Farms’ technical inefficiencies in the presence of government programs*

We focus on determining the impacts of government programs on farms’ technical inefficiency levels. We use Kumbhakar's stochastic frontier model that accounts for both production risks and risk preferences. Our theoretical framework shows that decoupled government transfers are likely to increase (decrease) DARA (IARA) farmers’ production inefficiencies if variable inputs are risk decreasing. However, the impacts of decoupled payments cannot be anticipated if variable inputs are risk increasing. We use farm‐level data collected in Kansas to illustrate the model.     

Investment planning under uncertainty and flexibility: the case of a purchasable sales contract*

Investment decisions are not only characterised by irreversibility and uncertainty but also by flexibility with regard to the timing of the investment. This paper describes how stochastic simulation can be successfully integrated into a backward recursive programming approach in the context of flexible investment planning. We apply this hybrid approach to a marketing question from primary production which can be viewed as an investment problem: should grain farmers purchase sales contracts which guarantee fixed product prices over the next 10 years? The model results support the conclusion from dynamic investment theory that it is essential to take simultaneously account of uncertainty and flexibility.