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Mathematics at Leeds University

# Paul Martin's Ethical Finance Project Links Page

The objective is to construct a mathematical model of certain financial tools
(you choose which)
through which ethical considerations about these tools can be
articulated.

The aim is to
model accurately enough, so that ethically `preferable' tools can be designed.

The challenge is to define the ethical considerations tightly enough
that they can be articulated in a mathematical model. This might
require a good understanding of the (social?) context of each
ethical component. (Such as can sometimes be found in the
ethical formulations of Sharia, for example.)
## Our base model

An n-commodity marked `with money' (local-universal unit)

=
point x in n-dimensional vector space (money values of commodities)
A person

=
point y in n+m-dimensional vector space (holdings including money,
influence etc)

QUESTION:
but does it make sense for all commodity prices to go up (or all down)?
(Inflation/deflation//only when dynamics comes in.)

Wealth of person in market (in money units)

= (1,x,...)(y_0, y_1, y_2, ...)^t where y_0 is money.

Now x = x(t), so wealth is also time dependent.

QUESTION: does x(t) behave like a Brownian particle with drift in a field?

y=y(t) by trading^* and by wealth creation and use.

(* assume all trades use market, so are instantaneously wealth neutral.)

There is possible lag in applying market at point of trade - but
probably can neglect this.

- 1. revise linear algebra and vector spaces.
- 2. revise elementary particle motion.
- 3. analyse financial tool
- 4. examine ethical considerations
- 5.

## project links: