How Financial . . . Limitations of the . . . Blockchain as an . . . Formulation of the . . . Blockchains Beyond Bitcoin: Notations Towards Optimal Level of Analysis of the Problem Let Us Find the . . . Decentralization in Storing Discussion Acknowledgments Financial Data Home Page Thach Ngoc Nguyen 1 , Olga Kosheleva 2 Title Page Vladik Kreinovich 2 , and Hoang Phuong Nguyen 3 ◭◭ ◮◮ 1 Banking University of Ho Chi Minh City, Vietnam, ◭ ◮ Thachnn@buh.edu.vn Page 1 of 14 2 University of Texas at El Paso, El Paso, Texas 79968, USA olgak@utep.edu, vladik@utep.edu Go Back 3 Division Informatics, Math-Informatics Faculty, Thang Long University, Hanoi, Vietnam, nhphuong2008@gmail.com Full Screen Close Quit
How Financial . . . Limitations of the . . . 1. How Financial Information Is Currently Stored Blockchain as an . . . • At present, usually, the information about each finan- Formulation of the . . . cial transaction is stored in three places: Notations Analysis of the Problem – with the buyer, Let Us Find the . . . – with the seller, and Discussion – with the bank. Acknowledgments Home Page • In many real-life financial transactions, a problem later appears. Title Page • So it becomes necessary to recover the information ◭◭ ◮◮ about the sale. ◭ ◮ • From this viewpoint, the current system of storing in- Page 2 of 14 formation is not fully reliable. Go Back Full Screen Close Quit
How Financial . . . Limitations of the . . . 2. Limitations of the Current Scheme Blockchain as an . . . • If a buyer has a problem, and his/her computer crashes Formulation of the . . . and deletes the original record, Notations Analysis of the Problem – the only neutral source of information is then the Let Us Find the . . . bank, Discussion – but the bank may have gone bankrupt since then. Acknowledgments • It is thus desirable to have more duplication, to in- Home Page crease the reliability of storing financial records. Title Page ◭◭ ◮◮ ◭ ◮ Page 3 of 14 Go Back Full Screen Close Quit
How Financial . . . Limitations of the . . . 3. Blockchain as an Absolutely Reliable – but Some- Blockchain as an . . . what Wasteful – Scheme for Storing Data Formulation of the . . . • The known reliable alternative to the usual scheme of Notations storing financial data is the blockchain scheme. Analysis of the Problem Let Us Find the . . . • It was originally designed for bitcoin transactions. Discussion • In this scheme, the record of each transaction is stored Acknowledgments at the location of every single participant. Home Page • This extreme duplication makes blockchains a very re- Title Page liable way of storing financial data. ◭◭ ◮◮ • On the other hand, in this scheme: ◭ ◮ – every time anyone performs a financial transaction, Page 4 of 14 – this information needs to be transmitted to all the nodes. Go Back • This takes a lot of computation time. Full Screen • So, from this viewpoint, this scheme is wasteful. Close Quit
How Financial . . . Limitations of the . . . 4. Formulation of the Problem Blockchain as an . . . • What scheme should we select to store the financial Formulation of the . . . data? Notations Analysis of the Problem • It would be nice to have our data stored in an abso- Let Us Find the . . . lutely reliable way. Discussion • Thus, it may seem reasonable to use blockchain for all Acknowledgments financial transactions, not just for bitcoins. Home Page • However, already for bitcoins, each world-wide update Title Page corresponding to each transaction takes about 10 sec- ◭◭ ◮◮ onds. ◭ ◮ • And bitcoins participate in only a small percentage of Page 5 of 14 financial transactions. Go Back • If we apply the same technique to all financial trans- actions, this delay would increase drastically. Full Screen Close Quit
How Financial . . . Limitations of the . . . 5. Formulation of the Problem (cont-d) Blockchain as an . . . • The resulting hours of delay will make the system com- Formulation of the . . . pletely impractical. Notations Analysis of the Problem • So, it is desirable to find the optimal level of duplication Let Us Find the . . . for each financial transaction. Discussion • This level may be different for different transactions. Acknowledgments Home Page • When a customer buys a relatively cheap product, too much duplication probably does not make sense. Title Page • The risk is small but the need for additional storage ◭◭ ◮◮ would increase the cost. ◭ ◮ • On the other hand, for an expensive purchase, we may Page 6 of 14 want to spend a little more to decrease the risk. Go Back • This is similar to how we buy insurance when we buy Full Screen a house or a car. Close Quit
How Financial . . . Limitations of the . . . 6. Formulation of the Problem (cont-d) Blockchain as an . . . • Good news is that the blockchain scheme itself – with Formulation of the . . . its encryptions etc. – does not depend on Notations Analysis of the Problem – whether we store each transaction at every node Let Us Find the . . . – or only in some selected nodes. Discussion • In this sense, the technology is there, no matter what Acknowledgments level of duplication we choose. Home Page • The only problem is to find the optimal duplication Title Page level. ◭◭ ◮◮ • In this paper, we show how to find the optimal level of ◭ ◮ duplication for each type of financial transaction. Page 7 of 14 Go Back Full Screen Close Quit
How Financial . . . Limitations of the . . . 7. Notations Blockchain as an . . . • Let d denote the level of duplication. Formulation of the . . . Notations • So d is the number of copies of the original transaction Analysis of the Problem record that will be independently stored. Let Us Find the . . . • Let p be the probability that each copy can be lost. Discussion • This probability can be estimated based on experience. Acknowledgments Home Page • Let c denote the total cost of storing one copy of the Title Page transaction record. ◭◭ ◮◮ • Finally, let L be the expected financial loss that will happen if: ◭ ◮ Page 8 of 14 – a problem emerges related to the original sale, and – all the copies of the corresponding record have dis- Go Back appeared. Full Screen Close Quit
How Financial . . . Limitations of the . . . 8. Notations (cont-d) Blockchain as an . . . • This expected financial loss L can estimated by multi- Formulation of the . . . plying: Notations Analysis of the Problem – the cost of the transaction and Let Us Find the . . . – the probability that the bought item will turn out Discussion to be faulty. Acknowledgments • The cost c of storing a copy is about the same for all Home Page the transactions, whether they are small or large. Title Page • On the other hand, the potential loss L depends on the ◭◭ ◮◮ size of the transaction – and on the corresponding risk. ◭ ◮ Page 9 of 14 Go Back Full Screen Close Quit
How Financial . . . Limitations of the . . . 9. Analysis of the Problem Blockchain as an . . . • Since the cost of storing one copy of the financial trans- Formulation of the . . . action is c , the cost of storing d copies is equal to d · c . Notations Analysis of the Problem • To this cost, we need to add the expected loss if all Let Us Find the . . . copies of the transaction are accidentally deleted. Discussion • For each copy, the probability that it will be acciden- Acknowledgments tally deleted is p . Home Page • The copies are assumed to be independent. Since we Title Page have d copies: ◭◭ ◮◮ – the probability that all d of them will be acciden- ◭ ◮ tally deleted is therefore equal to Page 10 of 14 – the product p d of the d probabilities p correspond- Go Back ing to each copy. Full Screen • So, we have the loss L with probability p d . Close Quit
How Financial . . . Limitations of the . . . 10. Analysis of the Problem (cont-d) Blockchain as an . . . • We have the loss L with probability p d . Formulation of the . . . Notations • Thus, the expected loss from losing all the copies of the record is equal to the product p d · L . Analysis of the Problem Let Us Find the . . . • Hence, once we have selected the number d of copies, Discussion the overall expected loss E is equal to E = d · c + p d · L. Acknowledgments Home Page • We need to find the value d for which this overall loss is the smallest possible. Title Page ◭◭ ◮◮ ◭ ◮ Page 11 of 14 Go Back Full Screen Close Quit
How Financial . . . Limitations of the . . . 11. Let Us Find the Optimal Level of Duplication Blockchain as an . . . • To find the optimal d , we equate the derivative of the Formulation of the . . . above expression with respect to 0; then: Notations Analysis of the Problem | ln( p ) | · ln( L ) + ln | ln( p ) | − ln( c ) 1 d = . Let Us Find the . . . | ln( p ) | Discussion • As one can easily see, the larger the expected loss L , Acknowledgments the more duplications we need. Home Page • In general, the number of duplications is proportional Title Page to the logarithm of the expected loss. ◭◭ ◮◮ ◭ ◮ Page 12 of 14 Go Back Full Screen Close Quit
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