The Effects of Random and Seasonal Environmental Fluctuations on Optimal Harvesting and Stocking

Abstract. We analyze the harvesting and stocking of a population that is affected by random and seasonal environmental fluctuations. The main novlty comes from having three layers of environmental fluctuations. The first layer is due to the environment switching at random times between different environmental states. This is similar to having sudden environmental changes or catastrophes. The second layer is due to seasonal variation, where there is a significant change in the dynamics between seasons. Finally, the third layer is due to the constant presence of environmental stochasticity|between the seasonal or random regime switches, the species is affected by fluctuations which can be modelled by white noise. This framework is more realistic because it can capture both significant random and deterministic environmental shifts as well as small and frequent uctuations in abiotic factors. Our framework also allows for the price or cost of harvesting to change deterministically and stochastically, something that is more realistic from an economic point of view. The combined effects of seasonal and random fluctuations make it impossible to find the optimal harvesting-stocking strategy analytically. We get around this roadblock by developing rigorous numerical approximations and proving that they converge to the optimal harvesting-stocking strategy. We apply our methods to multiple population models and explore how prices, or costs, and environmental fluctuations in uence the optimal harvesting-stocking strategy. We show that in many situations the optimal way of harvesting and stocking is not of threshold type

Spatial and stochastic epidemics : theory, simulation and control

It is now widely acknowledged that spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In this work I investigate an ensemble of techniques for understanding the stochastic dynamics of spatial and discrete epidemic processes, with especial consideration given to SIR disease dynamics for the Levins-type metapopulation. I present a toolbox of techniques for the modeller of spatial epidemics. The highlight results are a novel form of moment closure derived directly from a stochastic differential representation of the epidemic, a stochastic simulation algorithm that asymptotically in system size greatly out-performs existing simulation methods for the spatial epidemic and finally a method for tackling optimal vaccination scheduling problems for controlling the spread of an invasive pathogen

Applications of Stochastic Control in Energy Real Options and Market Illiquidity

We present three interesting applications of stochastic control in finance. The first is a real option model that considers the optimal entry into and subsequent operation of a biofuel production facility. We derive the associated Hamilton Jacobi Bellman (HJB) equation for the entry and operating decisions along with the econometric analysis of the stochastic price inputs. We follow with a Monte Carlo analysis of the risk profile for the facility. The second application expands on the analysis of the biofuel facility to account for the associated regulatory and taxation uncertainty experienced by players in the renewables and energy industries. A federal biofuel production subsidy per gallon has been available to producers for many years but the subsidy price level has changed repeatedly. We model this uncertain price as a jump process. We present and solve the HJB equations for the associated multidimensional jump diffusion problem which also addresses the model uncertainty pervasive in real option problems such as these. The novel real option framework we present has many applications for industry practitioners and policy makers dealing with country risk or regulatory uncertainty---which is a very real problem in our current global environment. Our final application (which, although apparently different from the first two applications, uses the same tools) addresses the problem of producing reliable bid-ask spreads for derivatives in illiquid markets. We focus on the hedging of over the counter (OTC) equity derivatives where the underlying assets realistically have transaction costs and possible illiquidity which standard finance models such as Black-Scholes neglect. We present a model for hedging under market impact (such as bid-ask spreads, order book depth, liquidity) using temporary and permanent equity price impact functions and derive the associated HJB equations for the problem. This model transitions from continuous to impulse trading (control) with the introduction of fixed trading costs. We then price and hedge via the economically sound framework of utility indifference pricing. The problem of hedging under liquidity impact is an on-going concern of market makers following the Global Financial Crisis

Dynamic scholastic control applications in finance and insurance

Control theory has gained a widespread use in almost every area of decision making problems. In this thesis, we seek to construct a premium setting strategy and an asset allocation strategy of a non-life insurance company whose goal is to maximise a metric of her utility function. As insurance companies do not have perfect insight into future market and cannot assume any given scenario with certainty, stochasticity is introduced to model the market conditions and the risk processes that the running of the insurance business is subject to. The problem is formulated as a continuous time and continuous space control problem where the state process is controlled continuously in a way to achieve the target. Bellman optimality principle in a stochastic environment is used to reduce the continuous time decision problem into a fixed point decision problem under the umbrella of Hamilton- Jacobi-Bellman equation. We also consider the pricing of financial derivative products written on catastrophe losses. Since the market of catastrophe insurance is incomplete, we make use of the concept of indifference of utility theory of a market participant to derive the so-called affordable price

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Increasing Risk: Dynamic Mean-Preserving Spreads

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean-Preserving Spreads to a dynamic framework. We adapt the original integral conditions to transition probability densities, and give sufficient conditions for their satisfaction. We then prove that a specific nonlinear scalar diffusion process, super-diffusive ballistic noise, is the unique process that satisfies the integral conditions among a broad class of processes. This process can be generated by a random superposition of linear Markov processes with constant drifts. This exceptionally simple representation enables us to systematically revisit, by means of the properties of Dynamic Mean-Preserving Spreads, four workhorse economic models originally based on White Gaussian Noise

Incremental sampling based algorithms for state estimation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 95-98).Perception is a crucial aspect of the operation of autonomous vehicles. With a multitude of different sources of sensor data, it becomes important to have algorithms which can process the available information quickly and provide a timely solution. Also, an inherently continuous world is sensed by robot sensors and converted into discrete packets of information. Algorithms that can take advantage of this setup, i.e., which have a sound founding in continuous time formulations but which can effectively discretize the available information in an incremental manner according to different requirements can potentially outperform conventional perception frameworks. Inspired from recent results in motion planning algorithms, this thesis aims to address these two aspects of the problem of robot perception, through novel incremental and anytime algorithms. The first part of the thesis deals with algorithms for different estimation problems, such as filtering, smoothing, and trajectory decoding. They share the basic idea that a general continuous-time system can be approximated by a sequence of discrete Markov chains that converge in a suitable sense to the original continuous time stochastic system. This discretization is obtained through intuitive rules motivated by physics and is very easy to implement in practice. Incremental algorithms for the above problems can then be formulated on these discrete systems whose solutions converge to the solution of the original problem. A similar construction is used to explore control of partially observable processes in the latter part of the thesis. A general continuous time control problem in this case is approximates by a sequence of discrete partially observable Markov decision processes (POMDPs), in such a way that the trajectories of the POMDPs -- i.e., the trajectories of beliefs -- converge to the trajectories of the original continuous problem. Modern point-based solvers are used to approximate control policies for each of these discrete problems and it is shown that these control policies converge to the optimal control policy of the original problem in an appropriate space. This approach is promising because instead of solving a large POMDP problem from scratch, which is PSPACE-hard, approximate solutions of smaller problems can be used to guide the search for the optimal control policy.by Pratik Chaudhari.S.M

Contingent Claim Pricing with Applications to Financial Risk Management

Contingent Claim Pricing with Applications to Financial Risk Management By Hua Chen 2008 Committee Chair: Samuel H. Cox and Shaun Wang Major Academic Unit: Department of Risk Management and Insurance This is a multi-essay dissertation designed to explore the contingent claim pricing theory with non-tradable underlying assets, with emphasis on its applications to insurance and risk management. In the first essay, I apply the real option pricing theory and dynamic programming methods to address problems in the area of operational risk management. Particularly, I develop a two-stage model to help firms determine optimal switching triggers in the event of an influenza epidemic. In the second essay, I examine mortality securitization in an incomplete market framework. I build a jump-diffusion process into the original Lee-Carter model and explore alternative model with transitory versus permanent jump effects. I discuss pricing difficulties of the Swiss Re mortality bond (2003) and use the Wang transform to account for correlations of the mortality index over time. In the third essay, I study the valuation of the non-recourse provision in reverse mortgages. I model the various risks embedded in the HECM program and apply the conditional Esscher transform to price the non-recourse provision. I further examine the premium structure of HECM loans and investigate whether insurance premiums are adequate to cover expected claims

A neural network approach to high-dimensional optimal switching problems with jumps in energy markets

We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sub-linear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problems