Martingales and Financial Mathematics

In this expository paper, we will discuss the role played by martingales in Financial Mathematics. More precisely, we will restrict ourselves to a mathematical formulation of the economical concept of an arbitrage-free, complete market and the pricing of derivatives in such models. For a clear exposition, we only consider the discrete case. We also discuss the Cox-Ross-Rubinstein model which is still one of the most used models in Finance

Modeling Total Maintenance Cost of a Repairable System in Some Bounded Time Interval

In this paper we model the total maintenance cost of a repairable system where the inter-maintenance times are modeled as discrete-time and continuous-time renewal processes. The maintenance cost is assumed to be a function of the lifetime of the system. We derive the probability distribution, including the mean and the variance, of the total maintenance cost. The results are presented in the form of generating functions and Laplace transforms that in general have to be inverted numerically. Some examples are presented in this paper

A low-bias simulation scheme for the SABR stochastic volatility model

The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop an lowbias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation

Statistical Modelling of Pitting Corrosion: Extrapolation of the Maximum Pit Depth-Growth

Pitting corrosion is one of the main threats in the pressure vessels integrity and also causes the failure of buried pipelines steels that transport sour gas, crude oil or condensate hydrocarbon, for this reason, a reliability assessment of pressurized vessels and buried pipelines based on probabilistic mathematical modelling to estimate the remaining life-time due to pitting corrosion damage is extensively employed. Herein, a methodology for probabilistic mathematical modelling of the pits initiation process and its depth growth process is developed; both uncertain processes are well represented by stochastic models. In this methodology two stochastic models are applied; Poisson process is used to model pit initiation and Gamma process to model the pit depth-growth. Such methods are validated using data produced by computer modeling procedures. On the other hand, in the oil industry it is common not to inspect the entire vessels surface; instead of this only a small part of the surface is under inspection. According to this, the use of Block Maxima (BM) and Peak-Over-Threshold (POT) models “EXTREME VALUE STATISTICS” to characterize the probability distribution of maximum pit depths is also approached. The results indicate that POT model can evaluate efficiently the maximum pitting corrosion depths.Aknowledge and express their gratitude to CONACyT for the SNI distinction as research membership and the monthly stipend received

Effecten van garnalenvisserij in Natura 2000 gebieden

De garnalenvisserij is economisch en in aantallen schepen één van de belangrijkste visserijen in Nederland en opereert vooral binnen Natura 2000 gebieden. Voor zowel de Noordzeekustzone als de Waddenzee is er binnen de Natura 2000 wetgeving een verbeterdoelstelling geformuleerd voor Habitattype 1110 (permanent overstroomde zandbanken). Het effect van het garnalentuig op het ecosysteem is echter niet goed bekend. Om in dit kennishiaat te voorzien, is er in de periode 2012-2014 onderzoek uitgevoerd naar een aantal aspecten van de mogelijke effecten van de garnalenvisserij. Enerzijds is de bijvangst in kaart gebracht, anderzijds is experimenteel onderzoek verricht naar de korte termijneffecten van het garnalentuig op de bodemfauna

Duurzame maïsteelt op zandgrond : verslag van een deskundigendag, gehouden op 22 april 2010

Voor de melkveehouderij op zandgrond is de maïsteelt belangrijk. Zetmeelrijke, eiwitarme maïs combineert uitstekend met zetmeelarm maar eiwitrijk gras, wat goed is voor de koe maar ook voor het milieu omdat een maïsgewas zeer efficiënt met water omgaat en omdat een rantsoen met maïs de emissies van lachgas en ammoniak beperkt. Bovendien kan door de voeding van maïs op krachtvoer worden bespaard. Daar staat tegenover dat op veel bedrijven bij de maïsteelt te veel meststoffen en herbiciden naar het grond- en oppervlaktewater verloren gaan. Dat maakt het voor waterbeheerders moeilijk te voldoen aan de kwaliteitsnormen die de Kaderrichtlijn Water (KRW) stelt. Ook de maïstelers zijn daar niet blij mee, omdat dit duidt op een slechte benutting van grondstoffen. De teeltkosten zijn dan te hoog, de gewasopbrengsten te laag, of de bodemkwaliteit lijdt eronder

Stochastic processes and point processes of excursions

Electrical Engineering, Mathematics and Computer Scienc

Indonesian options

Jakarta Stock Exchange Indonesia has started to trade Indonesian options at September 9th, 2004. An Indonesian option can be considered as an American style barrier option with immediate (forced) exercise if the price hits or crosses the barrier before maturity. The payoff of the option is based on a moving average of the price of the underlying stock. The barrier is fixed at the strike price plus or minus a 10 percent. The option is automatically exercised when the underlying stock hits or crosses the barrier and the difference between strike and barrier is paid immediately. We will refer to type of this option as Indonesian option. In this paper we study the pricing of the Indonesian option in a Black-Scholes economy. We will derive analytic approximations for the option price. We will discuss volatility and it turns out that expression we cannot calculate the implied volatilities.Electrical Engineering, Mathematics and Computer Scienc