Department of Business and Management Science
http://hdl.handle.net/11250/163542
Thu, 18 Jan 2018 04:19:24 GMT2018-01-18T04:19:24ZHarvesting in a Fishery with Stochastic Growth and a Mean-Reverting Price
http://hdl.handle.net/11250/2468585
Harvesting in a Fishery with Stochastic Growth and a Mean-Reverting Price
Kvamsdal, Sturla F; Poudel, Diwakar; Sandal, Leif Kristoffer
We analyze a continuous, nonlinear bioeconomic model to demonstrate how stochasticity in the growth of fish stocks affects the optimal exploitation policy when prices are stochastic, mean-reverting and possibly harvest dependent. Optimal exploitation has nonlinear responses to the price signal and should be conservative at low levels of biological stochasticity and aggressive at high levels. Price stochasticity induces conservative exploitation with little or no biological uncertainty, but has no strong effect when the biological uncertainty is larger. We further observe that resource exploitation should be conservative when the price reverts slowly to the mean. Simulations show that, in the long run, both the stock level and the exploitation rate are lower than in the deterministic solution. With a harvest-dependent price, the long-run price is higher in the stochastic system. The price mean reversion rate has no influence on the long-run solutions.
Key words Feedback policy, fisheries management, Hamilton-Jacobi-Bellman approach, mean-reversion, stochastic optimization.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11250/24685852014-01-01T00:00:00ZCreaming - and the depletion of resources: A Bayesian data analysis
http://hdl.handle.net/11250/2466710
Creaming - and the depletion of resources: A Bayesian data analysis
Lillestøl, Jostein; Sinding-Larsen, Richard
This paper considers sampling in proportion to size from a partly unknown distribution. The applied context is the exploration for undiscovered resources, like oil accumulations in different deposits, where the most promising deposits are likely to be drilled first, based on some geologic size indicators (“creaming”). A Log-normal size model with exponentially decaying creaming factor turns out to have nice analytical features in this context, and fits well available data, as demonstrated in Lillestøl and Sinding-Larsen (2017). This paper is a Bayesian follow-up, which provides posterior parameter densities and predictive densities of future discoveries, in the case of uninformative prior distributions. The theory is applied to the prediction of remaining petroleum accumulations to be found on the mature part of the Norwegian Continental Shelf.
Thu, 16 Nov 2017 00:00:00 GMThttp://hdl.handle.net/11250/24667102017-11-16T00:00:00ZOptimal multi-dimensional stochastic harvesting with density-dependent prices
http://hdl.handle.net/11250/2466585
Optimal multi-dimensional stochastic harvesting with density-dependent prices
Alvarez, Luis H.; Lungu, Edward; Øksendal, Bernt
We prove a verification theorem for a class of singular control problems which model
optimal harvesting with density-dependent prices or optimal dividend policy with capitaldependent
utilities. The result is applied to solve explicitly some examples of such optimal
harvesting/optimal dividend problems.
In particular, we show that if the unit price decreases with population density, then the
optimal harvesting policy may not exist in the ordinary sense, but can be expressed as a
”chattering policy”, i.e. the limit as ∆x and ∆t go to 0 of taking out a sequence of small
quantities of size ∆x within small time periods of size ∆t.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11250/24665852016-01-01T00:00:00ZOil Prices and the Renewable Energy Sector
http://hdl.handle.net/11250/2466261
Oil Prices and the Renewable Energy Sector
Kyritsis, Evangelos; Serletis, Apostolos
Energy security, climate change, and growing energy demand issues are moving up on the global political agenda, and contribute to the rapid growth of the renewable energy sector. In this paper we investigate the effects of oil price shocks, and also of uncertainty about oil prices, on the stock returns of clean energy and technology companies. In doing so, we use monthly data that span the period from May 1983 to December 2016, and a bivariate structural VAR model that is modified to accommodate GARCH-in-mean errors, and it is used to generate impulse response functions. Moreover, we examine the asymmetry of stock responses to oil price shocks and compare them accounting for oil price uncertainty, while effects of oil price shocks of different magnitude are also investigated. Our evidence indicates that oil price uncertainty has no statistically significant effect on stock returns, and that the relationship between oil prices and stock returns is symmetric. Our results are robust to alternative model specifications and stock prices of clean energy companies.
Tue, 14 Nov 2017 00:00:00 GMThttp://hdl.handle.net/11250/24662612017-11-14T00:00:00ZOptimal control of systems with noisy memory and BSDEs with Malliavin derivatives
http://hdl.handle.net/11250/2466169
Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives
Øksendal, Bernt; Mohammed, Salah-Eldin; Røse, Elin Engen; Dahl, Kristina Rognlien
In this article we consider a stochastic optimal control problem where
the dynamics of the state process, X(t), is a controlled stochastic differential
equation with jumps, delay and noisy memory. The term noisy
memory is, to the best of our knowledge, new. By this we mean that the
dynamics of X(t) depend on R t
t−δ X(s)dB(s) (where B(t) is a Brownian
motion). Hence, the dependence is noisy because of the Brownian motion,
and it involves memory due to the influence from the previous values of
the state process.
We derive necessary and sufficient maximum principles for this stochastic
control problem in two different ways, resulting in two sets of maximum
principles. The first set of maximum principles is derived using Malliavin
calculus techniques, while the second set comes from reduction to a discrete
delay optimal control problem, and application of previously known
results by Øksendal, Sulem and Zhang. The maximum principles also
apply to the case where the controller has only partial information, in the
sense that the admissible controls are adapted to a sub-σ-algebra of the
natural filtration.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11250/24661692016-01-01T00:00:00ZA Donsker delta functional approach to optimal insider control and applications to finance
http://hdl.handle.net/11250/2466127
A Donsker delta functional approach to optimal insider control and applications to finance
Draouil, Olfa; Øksendal, Bernt
We study optimal insider control problems, i.e. optimal control problems of stochastic
systems where the controller at any time t, in addition to knowledge about the
history of the system up to this time, also has additional information related to a
future value of the system. Since this puts the associated controlled systems outside
the context of semimartingales, we apply anticipative white noise analysis, including
forward integration and Hida-Malliavin calculus to study the problem. Combining this
with Donsker delta functionals we transform the insider control problem into a classical
(but parametrised) adapted control system, albeit with a non-classical performance
functional. We establish a sufficient and a necessary maximum principle for such systems.
Then we apply the results to obtain explicit solutions for some optimal insider
portfolio problems in financial markets described by Itˆo-L´evy processes. Finally, in the
Appendix we give a brief survey of the concepts and results we need from the theory
of white noise, forward integrals and Hida-Malliavin calculus.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11250/24661272015-01-01T00:00:00ZOptimal control of predictive mean-field equations and applications to finance
http://hdl.handle.net/11250/2466098
Optimal control of predictive mean-field equations and applications to finance
Øksendal, Bernt; Sulem, Agnès
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a predictive mean-field backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of the BSDE at time t may depend not just upon the unknown processes Y(t),Z(t),K(t,⋅), but also on the predicted future value Y(t+δ), defined by the conditional expectation A(t):=E[Y(t+δ)|Ft]. We give a sufficient and a necessary maximum principle for the optimal control of such systems, and then we apply these results to the following two problems: (i) Optimal portfolio in a financial market with an insider influenced asset price process. (ii) Optimal consumption rate from a cash flow modeled as a geometric Itô-Lévy SDE, with respect to predictive recursive utility.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11250/24660982016-01-01T00:00:00ZPlanning for charters: A stochastic maritime fleet composition and deployment problem
http://hdl.handle.net/11250/2466060
Planning for charters: A stochastic maritime fleet composition and deployment problem
Wang, Xin; Fagerholt, Kjetil; Wallace, Stein W.
This paper introduces a chartering problem that arises in the shipping industry. The chartering decisions determine the time-charter contracts to enter into, in particular, how many ships of each type to charter in, and for how long they are to be hired. We show that this problem can be modeled as a tactical fleet composition problem, with integrated fleet deployment and speed optimization, which also takes into account market uncertainties. We propose a two-stage stochastic programming model, and present a computational study based on the case of Odfjell, a leading chemical shipping company based in Bergen, Norway. We show how the charter plans produced can change depending on different modeling choices. We also show why and how different charter plans affect the company's overall performance, in order to provide guidance in helping the company make its chartering decisions.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11250/24660602017-01-01T00:00:00ZA Maximum Principle for Mean-Field SDEs with Time Change
http://hdl.handle.net/11250/2466053
A Maximum Principle for Mean-Field SDEs with Time Change
Di Nunno, Giulia; Haferkorn, Hannes Hagen
Time change is a powerful technique for generating noises and providing flexible models.
In the framework of time changed Brownian and Poisson random measures we study the
existence and uniqueness of a solution to a general mean-field stochastic differential equation.
We consider a mean-field stochastic control problem for mean-field controlled dynamics and
we present a necessary and a sufficient maximum principle. For this we study existence
and uniqueness of solutions to mean-field backward stochastic differential equations in the
context of time change. An example of a centralised control in an economy with specialised
sectors is provided.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11250/24660532017-01-01T00:00:00ZStepwise investment and capacity sizing under uncertainty
http://hdl.handle.net/11250/2464888
Stepwise investment and capacity sizing under uncertainty
Chronopoulos, Michail; Hagspiel, Verena; Fleten, Stein-Erik
The relationship between uncertainty and managerial flexibility is particularly crucial in addressing capital projects. We consider a firm that can invest in a project in either a single (lumpy investment) or multiple stages (stepwise investment) under price uncertainty and has discretion over not only the time of investment but also the size of the project. We confirm that if the capacity of a project is fixed and the investment premium associated with stepwise investment is positive, then lumpy investment becomes more valuable than a stepwise investment strategy under high price uncertainty. By contrast, if a firm has discretion over capacity, then we show that the stepwise investment strategy always dominates that of lumpy investment. In addition, we show that the total amount of installed capacity under a stepwise investment strategy is always greater than that under lumpy investment.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11250/24648882016-01-01T00:00:00Z