# Case for using mathematics

### The role of mathematics in generating wealth

Shipbuilding: for centuries people believed that they can build ships only using materials less dense than water so that it floats. This resulted in imposing limits on the size and power of steamers due to the vibration caused by long propellers shafts. However, Brunel, the great engineer, had a better understanding of the physics and mathematics of buoyancy. As a result, he succeeded to revolutionise the shipbuilding industry by building the first iron ship in the world, Great Britain, which also was the largest steamship of its day. Using mathematics, Brunel solved another problem with increasing the size of ships. The amount of coal required to power it across the Atlantic was believed to be so great that the volume of a large iron ship would need to be filled entirely with coal as it sales from either sides of the Atlantic. Brunel demonstrated the amount of coal required was proportional to the cross sectional area of the ship and that an increase in the volume of ship will not require an equal increase in coal consumption.

Derivatives market: the rise of the derivatives market is one of the most important financial phenomena in the recent history of the financial markets. Its expansion has been spectacularly rapid and large [see chart, note it only traces the growth of one class of derivatives].

According to Allbusiness.com, The evolution of financial derivatives during the past two decades ‘is related to the fundamental changes that have occurred in the financial markets. Innovations in financial theory and increased computerization, along with changes in the foreign exchange markets, the credit markets and the capital markets over this period, have contributed to the growth of financial derivatives. Since financial theory is essentially mathematical, an enormous wealth has been generated thanks to the application and understanding of the mathematics behind futures and options pricing. Even more interestingly, Robert Merton, the co-author of the famous Black-Scholes equation, admits that the equation was developed with “essentially no reference to empirical option pricing data as motivation for its formulation , it was a pure mathematical derivation based on past work by Louis Bachelier, Kiyoshi Ito and others.

"partial differential equations have become the core tools in a discipline that previously relied on a collection of anecdotes, rules of thumb, and shuffling of accounting data"

Despite of its theoretical character, his research determined future practices in the financial world. As Merton puts it “stochastic differential and integral equations, stochastic dynamic programming, and partial differential equations have become the core tools in a discipline that previously relied on a collection of anecdotes, rules of thumb, and shuffling of accounting data. The success of the Black-Stokes model was so great that Texas Instruments was selling calculators with the model pre-programmed only two years after its publication. Eventually, further research in pricing models increased the efficiency and the scope of the algorithms used and generated an almost unlimited range of innovative derivative products that are constantly launched on the financial markets.

### SERAFIM Ltd and Mathematics

We at SERAFIM Ltd believe that the oil and gas industry has a huge but inconspicuous opportunity in the application of mathematical thinking and derivations in disciplines as crucial to the industry as Reservoir Engineering and Financial Engineering (Project Finance particularly). It is impossible to imagine the world without the enormous wealth created thanks to innovations such as the large steel ships and derivatives. But it is certainly worth imagining the impact of the use of mathematical thinking on pushing the boundaries of the Oil and Gas E&P business. We help clients to achieve this by providing the tools to assess their prospects in a systemic way and to asses the profitability of these prospects using mathematical models that take account of more contextual factors than the, sometimes illusive, discount rate. We create algorithms to analyse complex geological and petrophysical data. We apply the SERAFIM approach to use a succession of simple mathematical models to complement "big" reservoir models. These simple models serve to build understanding, to identify approximately the optimal design and also help in the construction and quality control of the "big" models.

Our white papers (accessible from the menu on the left) demonstrate our achievements in the use of mathematics in the fields of our interest. Moreover, Serafim FUTURE, our Integrated Asset Model for Reservoir Engineers, offers a number of innovative algorithms that help numerous Reservoir Engineers around the glob with their day-to-day work.