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Financial Mathematics Reading Group 2010

Friday 22 January

Hessah Al-Motairi (LSE)

 

Irreversible capacity expansion with proportional and fixed costs

 

We consider the problem of determining the optimal capacity expansion strategy that a firm operating within a random economic environment should adopt. We model market uncertainty by means of a geometric Brownian motion. The objective is to maximise a performance criterion that involves a general running payoff function and associates a fixed and a proportional cost with each capacity increase. The resulting optimisation problem takes the form of a two-dimensional impulse control problem that we explicitly solve. 

 

 

Friday 5 February

Hessah Al-Motairi (LSE)

 

Irreversible capacity expansion with proportional and fixed costs

 

We consider the problem of determining the optimal capacity expansion strategy that a firm operating within a random economic environment should adopt. We model market uncertainty by means of a geometric Brownian motion. The objective is to maximise a performance criterion that involves a general running payoff function and associates a fixed and a proportional cost with each capacity increase. The resulting optimisation problem takes the form of a two-dimensional impulse control problem that we explicitly solve.

 

 

Friday 12 February 

Fares Al-Azemi (LSE)

 

Buy low and sell high strategy

 

 

Friday 19 February 

Neofytos Rodosthenous (LSE)

 

Pricing of Perpetual American Compound Options

We present explicit solutions to the perpetual American compound option problems in the Black-Merton-Scholes model. The method of proof is based on using the strong Markov property and reducing the initial optimal stopping problems to the associated free-boundary problems. We also obtain a closed form solution for the perpetual American chooser option problem, by means of the analysis of the equivalent two sided free-boundary problem. 

   
Friday 26 February
Fares Al-Azemi (LSE)
 

Buy low and sell high strategy 

   

Friday 5 March 

Polly Lon (LSE)

 

The stochastic goodwill problem: A monotone follower model with discretionary stopping 

 

We formulate and solve a problem that combines the features of the
so-called monotone follower of singular stochastic control theory with
optimal stopping.
In particular, we consider a stochastic system whose uncontrolled
state dynamics are modelled by a general one-dimensional Ito
diffusion.
The aim of the problem that we solve is to maximise the utility
derived from the system's state at the discretionary time when the
system's control is terminated. 

Friday 19 February 

Polly Lon (LSE) 

 

The stochastic goodwill problem: A monotone follower model with discretionary stopping 

 

We formulate and solve a problem that combines the features of the
so-called monotone follower of singular stochastic control theory with
optimal stopping.

In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Ito
diffusion.

The aim of the problem that we solve is to maximise the utility
derived from the system's state at the discretionary time when the
system's control is terminated. 

   

Tuesday 23 March 

Fares Al-Azemi (LSE) 

 

Buy low and sell high strategy  

   
   

Tuesday 23 March 

Neofytos Rodosthenous (LSE) 

 

Markov property 

   

Friday 30 April 

Polly Lon (LSE)

 

The stochastic goodwill problem: A monotone follower model with discretionary stopping  

 

We formulate and solve a problem that combines the features of the
so-called monotone follower of singular stochastic control theory with
optimal stopping.
In particular, we consider a stochastic system whose uncontrolled
state dynamics are modelled by a general one-dimensional Ito
diffusion.
The aim of the problem that we solve is to maximise the utility
derived from the system's state at the discretionary time when the
system's control is terminated.  

   

Friday 30 April 

Fares Al-Azemi (LSE)

 

Buy low and sell high strategy 

   

Tuesday 4 May 

Neofytos Rodosthenous (LSE)

 

Markov property  

   

Friday 11 June 

Elena Boguslavskaya (City University London)

 

A taste of combinatorics for probabilistic use 

 

Here we will talk about processes with independent increments, moments, cumulants, martingales, Bell polynomials, Appell polynomials and how helpful algebraic combinatorics can be for some problems in probability.

   

Friday 22 October 

Tom Bates (LSE)

 

Affine Term Structure Dynamics 

   

Friday 29 October 

Polly Lon (LSE)

 

Optimal stopping of a skew Brownian motion   

   

Thursday 9 December

Neofytos Rodosthenous (LSE)

 

No title

 

 

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