Friday 22 January

Hessah AlMotairi (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 twodimensional impulse control problem that we explicitly solve.



Friday 5 February

Hessah AlMotairi (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 twodimensional impulse control problem that we explicitly solve.



Friday 12 February

Fares AlAzemi (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 BlackMertonScholes model. The method of proof is based on using the strong Markov property and reducing the initial optimal stopping problems to the associated freeboundary 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 freeboundary problem.



Friday 26 February

Fares AlAzemi (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
socalled 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 onedimensional 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
socalled 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 onedimensional 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 AlAzemi (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
socalled 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 onedimensional 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 AlAzemi (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
