In computational finance, state-of-the-art numerical methods and computer methods are adopted to put a financial model into work. Methods like Monte-Carlo simulation, regression and machine learning are universal tools to simulate scenarios and access risks - one may use them for mathematical finance and climate models alike. Learning the numerical methods in finance gives one the tools needed to tackle climate models too.
But do we need financial modelling at all? Maybe you remember the fun question: "How much wealth would you have if you would have put $ 1 in a savings account 2000 years ago?" Investing at 1.5%, we would - theoretically - arrive at 8.6 trillion dollars! This behaviour reflects the time value of money - rational investors prefer to receive money today rather than the same amount of money in the future. It appears as if a small value today corresponds to a large value in the future, or, equivalently, a large value in the future corresponds to a small value today.
Such exponential growth is inherent to many simple financial models, used to value liabilities or future projects' costs and benefits.
However, what if we want to assess the impact of possible future damages? Think, for example, of the destruction caused by climatic calamities like hurricanes or floods in a given area. The probability of such extreme events has increased and will further increase due to climate change, and it is important to estimate the damage they would cause. Having in mind the idea of the time value of money described above, one could be tempted to discount the damage accordingly.
This discounting has, of course, a huge impact if we think about events in a quite far future, like twenty to hundred years: huge costs in the future appear to become small costs, and hence of a lower priority, today.
A consequence of this can be that one hazardously underestimates the priority to prevent future damages.
This is a dangerous misconception: while the valuation of a liability in the previously discussed form is well-grounded, it cannot be applied to access the priorities to fix or prevent future damages.
In , we try to tackle this problem by introducing a non-linear discounting for future damages. The so-called "discount factors" are different here, such that preventing environmental damages has a much higher priority.
This is an example of how an accurate understanding of mathematical finance is essential to comparing and understanding future scenarios.
Welcome to computational and mathematical finance.
 Christian Fries Discounting Damage:Non-Linear Discounting and Default Compensation, Preprint, 2021