 Okay. First, I'd like to thank the organizers for including our paper to this great conference. I'm Wei Jiang from Hong Kong University of Science and Technology. This is a joint work with Mindai from NUS, Stephen Coe from Boston University and Chongqing from Shuzhou University. So I'll talk to you about the economy of Bitcoin mining. As a knock model, the name in our title is the design of Bitcoin systems. So he mimicked the golden mining or natural resource mining to design the supplier in the Bitcoin system. So what we do is we try to leverage the classic hotel model for natural resource mining to investigate the Bitcoin mining. So first, Bitcoin, okay, we talk this quite a lot in this conference. It's actually a payment system with a peer-to-peer network. There are two groups of participants who play a very important role in this Bitcoin system. Why is, of course, users, they pay commission fees and enjoy transfer services. Users use Bitcoin for certain reasons. For example, the low cost of the transaction in Bitcoin system, the anonymous feature, fast transaction and the less regulation. And however, the other group of participants also play a very important role in the Bitcoin system. They are miners. So what they do is they provide verification service by validating the transaction orders submitted by users. And for their hard work, they get compensated in two ways. One is block rewards and the other is transaction fees. So let's check the detail about some data about block rewards. So there are two lines in this picture. The decline line shows the block rewards for each successfully mined block from time to time. So at the very beginning for each block, each successfully mined block, the miner will get 50 bitcoins as block rewards. But later it will decrease to be 25 for one block. And actually this block was halved every four years and eventually it will vanish. So as one can see, block rewards as one source of compensation to minus mining work is deterministic, is exogenous given in this system and it's scarce. It will terminate in a future year, 2140. So the scarcity in the Bitcoin supply implies that Bitcoin is an exhaustive resource. But let's check what happened for the transfer fees. So this figure, although the transfer fees in Bitcoin system and the Bitcoin transaction is paid in Bitcoin, but this figure shows the US dollars amount for daily transfer fees. So as one can see the transfer fees, it's very dynamic. It's actually in dollars determined by the Bitcoin system and it's unlimited. And you can see one daily amount transfer fee could be higher than one million US dollar. And actually it's the key incentive for miners after the end of the block rewards. So actually, although in the very beginning the designing of Bitcoin's mining or Bitcoin supply mimics the supply of gold. But actually the Bitcoin mining is quite different from the gold mining. First, in the friction sites, the Bitcoin miner will get the Bitcoin as a virtual asset. There's no storage costs. And in addition, the Bitcoin miner will suffer substantial liquidation costs. On the other hand, the gold mining, the miner will suffer significant storage costs, but usually low liquidation costs. And then in terms of output, the Bitcoin miner will usually come from predetermined block rewards and the additional has transfer fees, which is quite dynamic. But a traditional gold miner, they have no transfer fees from the mining business. And in addition, Bitcoin mining suffers uncertainly from mining lottery. And actually mining business is very competitive. Only one miner at one period can get the block rewards and transfers. But traditional gold mining has no such a lot of answering from a lottery feature. And most importantly for Bitcoin miner facing no storage costs and possibly high liquidation costs. So Bitcoin miner may prefer to adjust the inventory to maximize their return. In contrast, the traditional resource mining, like the gold miner facing the significant storage costs and low liquidation costs, they prefer to adjust the production. So the difference between Bitcoin mining and gold mining motivate us to study Bitcoin mining by clarifying its economic objective and investigate its policy space. And our research also motivated by two stylized facts about Bitcoin mining. The first one is about miners inventory. This figure shows the proportional inventory as shown by this black line. The proportional inventory is computed as the ratio of miners aggregate inventory time t divided by the cumulative Bitcoin supply time t. And this is the data we borrowed from Susan Assos working paper. So the denominator will increase by the block walls and the decrease by minus selling, but the denominator will also increase by minus block walls. So look at this ratio. If the minus selling rate is low, so this ratio will always increase due to the block walls to both nominate and denominator. But however, what we observe from data is this observe mining minus inventory keep declining, which implies that miner keeps selling their inventory inventory to users at a very high selling speed. So, so why this is the case. Is it due to the high volatility or due to some other uncertainty or risk in mining business we need to investigate. The second stylized facts is about average transfer fee rate as transfer fee as the second source to the to compensate Bitcoin miners. Actually, what we examine here is we examine the average transfer fee rate as showed by the red line which is computed as the ratio of a total transfer fees at time t divided by the process transfer transfer volume at time t. So, for a period from that, for example, from 2014 to 2016, as showed by this blue line the Bitcoin price is low then for this period with a low Bitcoin price, which implies that the demand for for Bitcoin transaction could be low then the average fee rate is actually flat. After 2016, when the Bitcoin price gradually climb up, and the Bitcoin transaction demand also increase, then the average fee rate increase dramatically. So, so why this fee rate is flat at the very beginning and then increase significantly later we we need to we need a model to interpret this actually we later we will show this is a beauty to several features one features about the the capacity issue as showed by this blue line blue line show the block size of in Bitcoin system so in the in the year before 2016 the block size is not full so the capacity in the Bitcoin system system is not full so in that period average fee rate is flat but after that when the Bitcoin transaction demand exceed the block capacity, then the average fee rate will increase dramatically. So motivated by this style as facts and the difference between Bitcoin mining and a good mining, we develop a continuous time dynamic model for Bitcoin mining by boring the idea of a classic hotel model for exhaustive resources. And our model to our best knowledge is the one of a month few of them could be calculated to America data and explain the formation to style as facts. Our model has implications like we found that high generics is one of major forces driving minus to set the Bitcoin holdings to an early stage even when Bitcoin price are quite low, and also our model suggests that a high Bitcoin demand leads to a high transaction fee rate. Okay, due to time constraint we skip the literature review, and then we will try to introduce our model. So our model is actually a resource of production model based on hotel is collected setting classes setting. Actually, the manager tried to maximize her profit via managing her inventory. So revenue where equals the price of the Bitcoin multiply the minus center rate, and that the cost is is two fold the liquidation cost and the running cost, and the Q is the minus center rate. The piece of Bitcoin price. H is the minus holding inventory. And then. So for, first, for the cost for the cost function here we focus, we first focus on the liquidation costs simply because the running costs does not affect this minus inventory strategy. But later in our extension of this business model where we introduce we incorporate the running costs and introduce an exit option to show that this running costs will affect the minus exit decision. But here we just focus on liquidation costs. So the Bitcoin, Bitcoin price exhaustively given but it's possible to see model as a linear function of based on minus Bitcoin transaction demand. This transaction demand is modeled as a jump diffusion process. And the minus holding inventory will increase as showed by this dynamics were increased by block walls and increased by transfer fees multiply the successful mining probability for this minor and then minus the setting rates. So for the Bitcoin price, actually it's usually viewed as an immediate change so we can simply use the quantity equation for money to, to model the Bitcoin price and post money so we assume it's a linear function of on the Bitcoin demand, and this data is determined by Bitcoin supply and the velocity. And the second for the Bitcoin transaction demand, we, it has it reflect two features from Bitcoin first Bitcoin is a kind of a new product or new product as a media of change. So the adoption of this Bitcoin, we are subject to an S shape diffusion process for new products. So we have this diffusion term for the, for the adoption of this Bitcoin transaction demand. Secondly, the Bitcoin is actually a non government back hit the media of change so it is usually subject to jump risk as exemplified in the wealth QJ paper on on non government back effect money. So we have this jump jump jump risk term. In addition, as we will exemplify later we will observe that the Bitcoin transaction demand has different regimes so we assume there are higher active regime and low active, active regime in the Bitcoin demand. Then the minus inventory is governed by this equation, the pie, the, the, the minus successful mining probability is given can be computed as a function of the minus computing power and the, the networks difficult difficulty level. And the BT, which measures the block words is a predetermined function decreasing function and it is the transaction fees we were model in the following slides. Actually, the base ideas will assume the, there are a lot of users. So, so we assume total volume of submit orders by all users is a linear function. This is an increase in function depend on the because demand shock, and also depends on the, on the inventory holding by all users. And then secondly we assume the users has our, our heterogeneous so they, they pay different level of transfers in their submit, submit, submitted orders so we assume there's a distribution of orders with the different free rate, which is given by this app. So we assume this blockchain, this big consistent has a capacity issue so each time a fixed number of orders can be processed by miners. So give this setup minus faces of an optimization problem by selecting fees with highest to maximize the transfer fees in in her candid block, such that the, the capacity will not be exceeded. So the base, the base idea is that all the, the miners will select the orders with highest the fees into her candid block until this block will be, be filled. So we will figure out an option free threshold. So when the total volume of submitted orders is less than the capacity, then order with the, if the order was there for you could be processed by if there's the demand that submit orders is higher than the capacity and only orders with high higher fees could be selected into the candidate, candidate block. So actually our, our model, our model about the minus fee collection mechanism is a social to a first price auction problem. And the optimal solution is a social with a symmetric Bayesian Nash equilibrium as a study ambassador pursue 2018 working paper. So if we have a model we, we can solve our model next. So, our model has this the solution has two cases in the short run case, because there are block words. So the minus value is where depends on the time. But in the long run case, there are no no block words anymore there are only transfer fees. So in this second case, the minus value does not depend on the time T. So the question of this problem has two implications. The first implication is so we can counter rise the minus optimal setting strategy by this equation. Actually the minus setting strategies is associated with two regions. Why is the center region. So when the big comprises higher than the margin value holding so the minor is in the center region. So they comprise a lower than the margin, lower than the margin value holding, then the minor we prefer to keep holding her inventory. So this figure shows that the case when there is no jump risk, then the left figure show shows the two regions for the minus strategy, the left figure shows the short short run case for example for the year 2014. And the right figure shows the long run case, which means there is no block words in in the future time. So as one can see, as one can see that this this setting barrier for the minus setting strategy implies that minor, when there's a low jump risk the minor play as a row as a buffer to supply the Bitcoin to users. So we want to examine what happened if there are high jump risk. So the left figure shows the minus setting barrier when there are high jump risk increase from zero to about 15. Then the salary, the minus setting barrier we were decreased dramatically to a very low level close to zero. This means high jump risk could motivate the minor to sell the holding to users at an early stage, even when Bitcoin price is low, but could the high voltage achieve such goal. It's actually not so likely as showed by the right figure, we, we let the jump risk to be zero, but we let the volatility increase from 50% to be to be 300%. The minus setting barrier only decreased by a by a relative low level. So which means high volatility is not able to motivate minors to sell their holding to to users at an early stage, even even when Bitcoin price is extremely low. And then the second implication of our model solution is we provide a categorization for minus value, even for minor with no block words in the future, future time, but later we will show the quantitative results. We will calibrate our model to the data. We use monthly data for like a big comprised minus aggregate inventory, market average fee rate aggregate aggregate transfer fee from the period 2013 to 2012. And for minus aggregate inventory, we only use data from 2013 to 2015. The reason is, after 2015 more and more minors are using the mixing strategy to hide their transaction records. So it's very difficult to to reveal their inventory from tracking their addresses in the Bitcoin system. Secondly, when we calibrated the model we will show we just use the model with the one minor the implication is in our previous in our previous model we it's a model for an individual minor. So if the system has a larger number of minor, if we assume different minor has the same mining probability, then numerical results show that even for these minors, they're mining their setting strategy is homogeneous approximate homogeneous regardless. of a different level of holding for different minors. So regarding this we can approximate combine this minor together so we use this model with only one minor to calibrate to the data. And this figure shows the memo pool transaction count, which is a proxy to the total volume submitted by users L in our model setup. So as observed from this memo pool transaction count it has different regimes, high regime, high active regime and low active regime. And then we calibrate our model to the data first for certain parameter we set the value for them for example the jump jump race we let the jump intensity to be 57 Z to be 0.9 which is equivalent to be a 10% downward jump. Once a week in a year. So this is the problem that we borrow from estimation existing literature which is actually a might one. And then for the rest parameters we try to match our model implied transfer fees and inventory with the observed transfer fees and inventory by minimize a this this square relative error term. So this is our calibration parameters, we, we want to show that our conversion results about inventory and average transfer fees. So in this figure the red line shows our model implied minus inventory that dash black line shows observe minus inventory so as one can see the model calibration can match the observed data. The reason is we, we show that jump risk could motivate a minor setting their holding to users at an early stage, even when become prices low. So this is the due to the jump risk. The second one is about the implied average fee rate showed by this red line and that the dashed line showed the observed data. So as one can see in this period from 2014 to 2016 the implied average fee rate is flat, simply due to the capacity issue because in this period, the capacity of the Bitcoin system is not filled. So, in this scenario, the average fee rate is flat. But after that when the Bitcoin demand transaction demand exceeds the capacity of the Bitcoin system, then the average fee rate increased dramatically. And our model calibration can can catch up the magnitude of the increase in the observed market average fee rate due to several settings. The one setting is we assume the users are heterogeneous so different user pay different level of transfers in there some, some media orders. Second one is we assume they're different regimes in the Bitcoin transaction transaction demand. So these two setting issues us our model can calibrate to the increase of the magnitude in the average fee rate. And then we show additional quantitative analysis about a quantity quantitative justification for minus value when the minus money the Bitcoin money are only compensated by transfer fees. So this figure in this figure we assume the minus inventory is zero. We assume there is a constant. We assume there is a constant demand shock. So as one can see, we plot the minus value from 2010 to 2016. So in the early stage, because the minus value is dominated by the block words. So the declining block words will will lead to declining minus value. So this is the in the first stage. But later when more and the more when the block words are decreasing dramatically and more and the more Bitcoin, Bitcoin also applied to minus and the minus setting more and more Bitcoin to users. Then the minus could able to collect more and the more transfer fees. So in the second stage minus value is dominated by the transfer fees. So we will see that this increasing transaction fees will lead to an increase minus value. And in a long run, then the block words there there are no block words anymore than the minus value is only decided by the transfer fees. So we can see because we assume a stable demand shock so in long run the minus value is decided by transfer fees is quite stable. And also we also show the results for different jump risk. So high jump risk could lower minus value, although the minus value is still in a U shape. Right, am I still. Okay. So, do I still have any few minutes. Okay, thank you. So then let's conclude. So we propose a model to study Bitcoin mining by extending the class of hotel model with inventory and the feedback supply. And we provide a quantitative justification of minus value based on own transfer fees and the block words and our model calibrated to data and can explain the dynamics average transfer rate and the minus inventory holding in observe data. And we also show jump risk is a key factor to understand the minus inventory holding. So thank you so much. And the questions are warmly welcome.