Problème de Snell et application aux options bermudiennes

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Substance Treatment Options in Psychosis (STOP) : a new intervention for dual diagnosis

Despite the high co-occurrence of psychosis and substance abuse, there is very little research on the development of effective treatments for this problem. This paper describes a new intervention that facilitates reaching functional goals through collaboration between therapists, participants and families. Substance Treatment Options in Psychosis (STOP) integrates pharmacological and psycho-logical treatments for psychotic symptoms, with cognitive-behavioural approaches to substance abuse. STOP is tailored to participants' problems and abilities, and recognises that control of consumption and even engagement may take several attempts. Training in relevant skills is augmented by bibliotherapy, social support and environmental change. A case description illustrates the issues and challenges in implementation.

The appropriateness of default investment options in defined contribution plans : Australian evidence

For participants in defined contribution (DC) plans who refrain from exercising investment choice, plan contributions are invested following the default investment option of their respective plans. Since default investment options of different plans vary widely in terms of their benchmark asset allocation, the most important determinant of investment performance, participants enrolled in these options face significantly different wealth outcomes at retirement. This paper simulates the terminal wealth outcomes under different static asset allocation strategies to evaluate their relative appeal as default investment choice in DC plans. We find that strategies with low or moderate allocation to stocks are consistently outperformed in terms of upside potential of exceeding the participant’s wealth accumulation target at retirement as well as downside risk of falling below that target outcome by aggressive strategies whose allocation to stocks approach 100%. The risk of extremely adverse wealth outcomes for plan participants also does not appear to be very sensitive to asset allocation. Our evidence suggests the appropriateness of strategies heavily tilted towards stocks to be nominated as default investment options in DC plans unless plan providers emphasize predictability of wealth outcomes over adequacy of retirement wealth.

Prognostic modelling options for remaining useful life estimation by industry

Over recent years a significant amount of research has been undertaken to develop prognostic models that can be used to predict the remaining useful life of engineering assets. Implementations by industry have only had limited success. By design, models are subject to specific assumptions and approximations, some of which are mathematical, while others relate to practical implementation issues such as the amount of data required to validate and verify a proposed model. Therefore, appropriate model selection for successful practical implementation requires not only a mathematical understanding of each model type, but also an appreciation of how a particular business intends to utilise a model and its outputs. This paper discusses business issues that need to be considered when selecting an appropriate modelling approach for trial. It also presents classification tables and process flow diagrams to assist industry and research personnel select appropriate prognostic models for predicting the remaining useful life of engineering assets within their specific business environment. The paper then explores the strengths and weaknesses of the main prognostics model classes to establish what makes them better suited to certain applications than to others and summarises how each have been applied to engineering prognostics. Consequently, this paper should provide a starting point for young researchers first considering options for remaining useful life prediction. The models described in this paper are Knowledge-based (expert and fuzzy), Life expectancy (stochastic and statistical), Artificial Neural Networks, and Physical models.

Lawyers' role options in family dispute resolution

Both family lawyers and family dispute resolution practitioners are“gatekeepers” to the family law system.In this article the authors explore,with reference to recent research, the characteristics shown to be present in successful collaborative relationships between these two groups of professionals. They then apply Rundle’s spectrum of contributions that lawyers can make to mediation to the family law context and explore the various role options for family lawyers in family dispute resolution.

Strategic project evaluation for open pit mining ventures using real options and allied econometric techniques

Open pit mine operations are complex businesses that demand a constant assessment of risk. This is because the value of a mine project is typically influenced by many underlying economic and physical uncertainties, such as metal prices, metal grades, costs, schedules, quantities, and environmental issues, among others, which are not known with much certainty at the beginning of the project. Hence, mining projects present a considerable challenge to those involved in associated investment decisions, such as the owners of the mine and other stakeholders. In general terms, when an option exists to acquire a new or operating mining project, , the owners and stock holders of the mine project need to know the value of the mining project, which is the fundamental criterion for making final decisions about going ahead with the venture capital. However, obtaining the mine project’s value is not an easy task. The reason for this is that sophisticated valuation and mine optimisation techniques, which combine advanced theories in geostatistics, statistics, engineering, economics and finance, among others, need to be used by the mine analyst or mine planner in order to assess and quantify the existing uncertainty and, consequently, the risk involved in the project investment. Furthermore, current valuation and mine optimisation techniques do not complement each other. That is valuation techniques based on real options (RO) analysis assume an expected (constant) metal grade and ore tonnage during a specified period, while mine optimisation (MO) techniques assume expected (constant) metal prices and mining costs. These assumptions are not totally correct since both sources of uncertainty—that of the orebody (metal grade and reserves of mineral), and that about the future behaviour of metal prices and mining costs—are the ones that have great impact on the value of any mining project. Consequently, the key objective of this thesis is twofold. The first objective consists of analysing and understanding the main sources of uncertainty in an open pit mining project, such as the orebody (in situ metal grade), mining costs and metal price uncertainties, and their effect on the final project value. The second objective consists of breaking down the wall of isolation between economic valuation and mine optimisation techniques in order to generate a novel open pit mine evaluation framework called the ―Integrated Valuation / Optimisation Framework (IVOF)‖. One important characteristic of this new framework is that it incorporates the RO and MO valuation techniques into a single integrated process that quantifies and describes uncertainty and risk in a mine project evaluation process, giving a more realistic estimate of the project’s value. To achieve this, novel and advanced engineering and econometric methods are used to integrate financial and geological uncertainty into dynamic risk forecasting measures. The proposed mine valuation/optimisation technique is then applied to a real gold disseminated open pit mine deposit to estimate its value in the face of orebody, mining costs and metal price uncertainties.

Options for the development of the New Zealand Law of Charities

The Australian Centre for Philanthropy and Nonprofit Studies was briefed to advise the Charities Commission of New Zealand on ways in which the law of charity might be developed. The substantive issue underpinning the brief is a need to enable charity law in New Zealand to continue to develop in accordance with the societal values of New Zealand. This is an options paper and as such it does not explain the current law, but is intended to generate constructive discussion. Four options are sketched, with important issues and implications for each. No recommendation is made to adopt a particular option; there are strengths and weaknesses, opportunities and threats with each of the four approaches canvassed.

Queensland Government Agency Libraries Review: Options Paper

The Queensland Government Agency Libraries Review was undertaken during the period January-June 2010. The research project was sponsored jointly by the Director-General, Department of the Premier and Cabinet, and the Director-General, Department of Public Works. The objective of the project was to examine future options for the Queensland Government library and research services that provide clients with efficient and cost-effective access to the information they need to conduct government business, to develop a picture of the services provided, the information resources managed, the client base and staffing. The review also considered the environmental factors impacting on contemporary government libraries to determine possible strategies that would ensure a strong and sustainable future for the services. The review process culminated in identifying potential options for future service delivery. The preferred option involves a proposal for the centralizing responsibility for the coordination of a network of Queensland Government Libraries and Research Centres (QGLR). The establishment of a network of research centres, with a central point for coordination of common strategies, systems and processes will enable library and research services to flow around individual agencies, and provide clearer avenues for multi-disciplinary work that characterises contemporary government policy and government services. The key elements of the proposal include the development of a single library and research portal for all government officers, which can be tailored to meet their particular research needs; increasing the visibility and accessibility of information and knowledge resources to those officers regardless of their agency affiliation; introducing better, more cost effective purchasing and licensing arrangements; and the potential to have a voice of influence in the strategic agenda for the government’s use of information and research.